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Constituents and Shapesof Nuclei and Nucleons Stanley Yen TRIUMF
Quick review of some quantum physics
1 Basic properties of waves
Frequency = number of crests passing by each second
velocity = frequency x wavelength
2 Waves can interfere with each other
amplitudes adding up = constructive interference amplitudes subtracting = destructive interference
copy The Internet Encyclopedia of Science httpwwwdaviddarlinginfoimages
copy Prof CK Ng University of Hong Kong httpwwwphyhkwikienglishhtmInterference2htm
nodal lines of completedestructive interferencewhere crest of one wavecancels out the troughof the second wave
3 Light is a wave because it shows interference
copy Florida State University
destructive interferencegives nodal lines(dark bands of zero light)just like the nodal linesin the case of water waves
4 Light is also a particle
The photoelectric effect shows that light is not a continuous wave but the light energy comes in packets of size
E = h f
where h = Plancks constant f = frequency of the light
low frequency (red) light = small packets of energy high frequency (blue ) = large packets of energy
E = 028 eV E = 049 eV
E = 10 7 eVE = 10-10 eV
6 Light is both particle and wave
This is a general property of all matter not just of light It is possible to see diffraction patterns made by beams of electrons neutrons protons carbon atoms and even Buckyballs
This is the fundamental principle of wave-particle duality
de Broglie
The wavelength is given by λ = h p
where h = Plancks constant p = momentum of the particle
7 The act of measurement disturbs the system being measured
eg measure the position of an electron by observing it with light of wavelength λ momentum p = hλ
When the photon scatters off the electron it imparts momentumto the electron so
Heisenberg uncertainty principle
large momentum p rarr short wavelength λ darr darr large distubance precise measurement of electron of position x darr darr uncertainty of electron uncertainty of electron momentum Δp asymp p position Δx asymp λ = hp
so Δp Δx asymp hMore precisely Δp Δx ge h4π
Similarly for energy and time ΔE Δt ge h4π
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
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-
Quick review of some quantum physics
1 Basic properties of waves
Frequency = number of crests passing by each second
velocity = frequency x wavelength
2 Waves can interfere with each other
amplitudes adding up = constructive interference amplitudes subtracting = destructive interference
copy The Internet Encyclopedia of Science httpwwwdaviddarlinginfoimages
copy Prof CK Ng University of Hong Kong httpwwwphyhkwikienglishhtmInterference2htm
nodal lines of completedestructive interferencewhere crest of one wavecancels out the troughof the second wave
3 Light is a wave because it shows interference
copy Florida State University
destructive interferencegives nodal lines(dark bands of zero light)just like the nodal linesin the case of water waves
4 Light is also a particle
The photoelectric effect shows that light is not a continuous wave but the light energy comes in packets of size
E = h f
where h = Plancks constant f = frequency of the light
low frequency (red) light = small packets of energy high frequency (blue ) = large packets of energy
E = 028 eV E = 049 eV
E = 10 7 eVE = 10-10 eV
6 Light is both particle and wave
This is a general property of all matter not just of light It is possible to see diffraction patterns made by beams of electrons neutrons protons carbon atoms and even Buckyballs
This is the fundamental principle of wave-particle duality
de Broglie
The wavelength is given by λ = h p
where h = Plancks constant p = momentum of the particle
7 The act of measurement disturbs the system being measured
eg measure the position of an electron by observing it with light of wavelength λ momentum p = hλ
When the photon scatters off the electron it imparts momentumto the electron so
Heisenberg uncertainty principle
large momentum p rarr short wavelength λ darr darr large distubance precise measurement of electron of position x darr darr uncertainty of electron uncertainty of electron momentum Δp asymp p position Δx asymp λ = hp
so Δp Δx asymp hMore precisely Δp Δx ge h4π
Similarly for energy and time ΔE Δt ge h4π
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
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- Slide 31
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- Slide 37
- Slide 38
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- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
2 Waves can interfere with each other
amplitudes adding up = constructive interference amplitudes subtracting = destructive interference
copy The Internet Encyclopedia of Science httpwwwdaviddarlinginfoimages
copy Prof CK Ng University of Hong Kong httpwwwphyhkwikienglishhtmInterference2htm
nodal lines of completedestructive interferencewhere crest of one wavecancels out the troughof the second wave
3 Light is a wave because it shows interference
copy Florida State University
destructive interferencegives nodal lines(dark bands of zero light)just like the nodal linesin the case of water waves
4 Light is also a particle
The photoelectric effect shows that light is not a continuous wave but the light energy comes in packets of size
E = h f
where h = Plancks constant f = frequency of the light
low frequency (red) light = small packets of energy high frequency (blue ) = large packets of energy
E = 028 eV E = 049 eV
E = 10 7 eVE = 10-10 eV
6 Light is both particle and wave
This is a general property of all matter not just of light It is possible to see diffraction patterns made by beams of electrons neutrons protons carbon atoms and even Buckyballs
This is the fundamental principle of wave-particle duality
de Broglie
The wavelength is given by λ = h p
where h = Plancks constant p = momentum of the particle
7 The act of measurement disturbs the system being measured
eg measure the position of an electron by observing it with light of wavelength λ momentum p = hλ
When the photon scatters off the electron it imparts momentumto the electron so
Heisenberg uncertainty principle
large momentum p rarr short wavelength λ darr darr large distubance precise measurement of electron of position x darr darr uncertainty of electron uncertainty of electron momentum Δp asymp p position Δx asymp λ = hp
so Δp Δx asymp hMore precisely Δp Δx ge h4π
Similarly for energy and time ΔE Δt ge h4π
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
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- Slide 54
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- Slide 56
- Slide 57
- Slide 58
-
copy Prof CK Ng University of Hong Kong httpwwwphyhkwikienglishhtmInterference2htm
nodal lines of completedestructive interferencewhere crest of one wavecancels out the troughof the second wave
3 Light is a wave because it shows interference
copy Florida State University
destructive interferencegives nodal lines(dark bands of zero light)just like the nodal linesin the case of water waves
4 Light is also a particle
The photoelectric effect shows that light is not a continuous wave but the light energy comes in packets of size
E = h f
where h = Plancks constant f = frequency of the light
low frequency (red) light = small packets of energy high frequency (blue ) = large packets of energy
E = 028 eV E = 049 eV
E = 10 7 eVE = 10-10 eV
6 Light is both particle and wave
This is a general property of all matter not just of light It is possible to see diffraction patterns made by beams of electrons neutrons protons carbon atoms and even Buckyballs
This is the fundamental principle of wave-particle duality
de Broglie
The wavelength is given by λ = h p
where h = Plancks constant p = momentum of the particle
7 The act of measurement disturbs the system being measured
eg measure the position of an electron by observing it with light of wavelength λ momentum p = hλ
When the photon scatters off the electron it imparts momentumto the electron so
Heisenberg uncertainty principle
large momentum p rarr short wavelength λ darr darr large distubance precise measurement of electron of position x darr darr uncertainty of electron uncertainty of electron momentum Δp asymp p position Δx asymp λ = hp
so Δp Δx asymp hMore precisely Δp Δx ge h4π
Similarly for energy and time ΔE Δt ge h4π
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
3 Light is a wave because it shows interference
copy Florida State University
destructive interferencegives nodal lines(dark bands of zero light)just like the nodal linesin the case of water waves
4 Light is also a particle
The photoelectric effect shows that light is not a continuous wave but the light energy comes in packets of size
E = h f
where h = Plancks constant f = frequency of the light
low frequency (red) light = small packets of energy high frequency (blue ) = large packets of energy
E = 028 eV E = 049 eV
E = 10 7 eVE = 10-10 eV
6 Light is both particle and wave
This is a general property of all matter not just of light It is possible to see diffraction patterns made by beams of electrons neutrons protons carbon atoms and even Buckyballs
This is the fundamental principle of wave-particle duality
de Broglie
The wavelength is given by λ = h p
where h = Plancks constant p = momentum of the particle
7 The act of measurement disturbs the system being measured
eg measure the position of an electron by observing it with light of wavelength λ momentum p = hλ
When the photon scatters off the electron it imparts momentumto the electron so
Heisenberg uncertainty principle
large momentum p rarr short wavelength λ darr darr large distubance precise measurement of electron of position x darr darr uncertainty of electron uncertainty of electron momentum Δp asymp p position Δx asymp λ = hp
so Δp Δx asymp hMore precisely Δp Δx ge h4π
Similarly for energy and time ΔE Δt ge h4π
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
4 Light is also a particle
The photoelectric effect shows that light is not a continuous wave but the light energy comes in packets of size
E = h f
where h = Plancks constant f = frequency of the light
low frequency (red) light = small packets of energy high frequency (blue ) = large packets of energy
E = 028 eV E = 049 eV
E = 10 7 eVE = 10-10 eV
6 Light is both particle and wave
This is a general property of all matter not just of light It is possible to see diffraction patterns made by beams of electrons neutrons protons carbon atoms and even Buckyballs
This is the fundamental principle of wave-particle duality
de Broglie
The wavelength is given by λ = h p
where h = Plancks constant p = momentum of the particle
7 The act of measurement disturbs the system being measured
eg measure the position of an electron by observing it with light of wavelength λ momentum p = hλ
When the photon scatters off the electron it imparts momentumto the electron so
Heisenberg uncertainty principle
large momentum p rarr short wavelength λ darr darr large distubance precise measurement of electron of position x darr darr uncertainty of electron uncertainty of electron momentum Δp asymp p position Δx asymp λ = hp
so Δp Δx asymp hMore precisely Δp Δx ge h4π
Similarly for energy and time ΔE Δt ge h4π
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
E = 028 eV E = 049 eV
E = 10 7 eVE = 10-10 eV
6 Light is both particle and wave
This is a general property of all matter not just of light It is possible to see diffraction patterns made by beams of electrons neutrons protons carbon atoms and even Buckyballs
This is the fundamental principle of wave-particle duality
de Broglie
The wavelength is given by λ = h p
where h = Plancks constant p = momentum of the particle
7 The act of measurement disturbs the system being measured
eg measure the position of an electron by observing it with light of wavelength λ momentum p = hλ
When the photon scatters off the electron it imparts momentumto the electron so
Heisenberg uncertainty principle
large momentum p rarr short wavelength λ darr darr large distubance precise measurement of electron of position x darr darr uncertainty of electron uncertainty of electron momentum Δp asymp p position Δx asymp λ = hp
so Δp Δx asymp hMore precisely Δp Δx ge h4π
Similarly for energy and time ΔE Δt ge h4π
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
6 Light is both particle and wave
This is a general property of all matter not just of light It is possible to see diffraction patterns made by beams of electrons neutrons protons carbon atoms and even Buckyballs
This is the fundamental principle of wave-particle duality
de Broglie
The wavelength is given by λ = h p
where h = Plancks constant p = momentum of the particle
7 The act of measurement disturbs the system being measured
eg measure the position of an electron by observing it with light of wavelength λ momentum p = hλ
When the photon scatters off the electron it imparts momentumto the electron so
Heisenberg uncertainty principle
large momentum p rarr short wavelength λ darr darr large distubance precise measurement of electron of position x darr darr uncertainty of electron uncertainty of electron momentum Δp asymp p position Δx asymp λ = hp
so Δp Δx asymp hMore precisely Δp Δx ge h4π
Similarly for energy and time ΔE Δt ge h4π
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
7 The act of measurement disturbs the system being measured
eg measure the position of an electron by observing it with light of wavelength λ momentum p = hλ
When the photon scatters off the electron it imparts momentumto the electron so
Heisenberg uncertainty principle
large momentum p rarr short wavelength λ darr darr large distubance precise measurement of electron of position x darr darr uncertainty of electron uncertainty of electron momentum Δp asymp p position Δx asymp λ = hp
so Δp Δx asymp hMore precisely Δp Δx ge h4π
Similarly for energy and time ΔE Δt ge h4π
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Heisenberg uncertainty principle
large momentum p rarr short wavelength λ darr darr large distubance precise measurement of electron of position x darr darr uncertainty of electron uncertainty of electron momentum Δp asymp p position Δx asymp λ = hp
so Δp Δx asymp hMore precisely Δp Δx ge h4π
Similarly for energy and time ΔE Δt ge h4π
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Plancks constant h sets the scale for the size of quantum effects
E = h f
λ = h p
Δp Δx ge h4π
ΔE Δt ge h4π
h = 6627x10-34 Joule-sec = 413x10-15 eV-sec
which is tiny compared to everyday life where typical energies are many Joules typical time are seconds
so the quantum effects are not normally apparent in everyday lifebecause they are too small
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
The deeper we go down thedistance scale from
crystalmoleculeatomatomic nucleusprotons amp neutronsquarks
the more apparent thesequantum effects are
Subatomic physics
= nuclear physics (study of the atomic nucleus)
+
particle physics (study of the elementary particles that make up nuclei and atoms)
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
We shall apply these principles of quantummechanics to several topics of subatomicphysics
the sizes and shapes of atomic nuclei the energy scale of nuclear processes the existence of quarks
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
1 The sizes and shapes of atomic nuclei
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
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- Slide 25
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- Slide 41
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- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
How do we see atoms and subatomic structureNot with this WHY NOT
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
How do we see atoms and subatomic structureNot with this WHY NOT
Because light is a wave it has a ldquofuzzinessrdquo the size of itswavelength and cannot resolve features smaller thanthat
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Why dont microwaves leak through themetal grill on the door
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Why dont microwaves leak through themetal grill on the door
Because the waves have a wavelength of 10 cm and cannotresolve the 2 mm holes in the grill As far as they are concernedthe grill is solid metal
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
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- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
How do we ldquoseerdquo whats inside an atomBy means of scattering experiments
Gold coins in haystack analogy to how Rutherford discoveredthe atomic nucleus
many smalldeflectionsof the projectiles
a few largedeflections --this is what theatom looks like
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Bullets through haystack picture not accurateActually cannot neglect the wavelike nature of the projectilesIn wave picture a scattering experiment looks like this
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
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- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Diffraction of water waves
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 51
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- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Diffraction of X-rays from powders of Al and NaCl(powder = many tiny crystals in random orientations)
Note that the intensity pattern for the two types of crystalsare different By mathematically working backwards fromthe diffraction pattern crystallographers can deduce thelocation of the atoms in the crystal
from CC Jones minervaunionedujonescScientifichtml
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
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- Slide 39
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- Slide 45
- Slide 46
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- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
To get an idea of how the diffraction pattern can tell us the size andshape of the nucleus consider the following demo
If the distance from onespeaker differs from thedistance from the other speaker by exactly 1 wavelengthor 2 wavelength etc
then the two crests arrive atthe same time and there isconstructive interference
If the distances differ bya half-integer from these valuesthen there will be destructiveinterference
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
nodallinesofcompletesilence
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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-
Lets try this demo with two loudspeakers
Download a freeware sound generator egSoundGen and set up 2 speakers about 100 cmapart generate sound at 880 Hz frequency(λ=039 m) and move your head around to find the nodallines at θ=230 (n=1) and θ=510 (n=2)
Reduce the separation between speakers to 50 cmand observe that the first nodal line moves outto θ=510
CONCLUSIONSmaller (more point-like) source results in wider diffraction pattern
Q What happens if we decrease the frequency
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
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- Slide 48
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- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
ikf∙r
Suppose the scattering centers are smeared out and described by density distribution ρ(r)In the case of charged particles interacting via the electric force ρ(r) is the charge densitydistribution
The total wave scattered in some direction is obtained by adding the waves from eachof the infinitesimal elements with the proper phase After some simple math we find
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
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- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Scattering Ratefor extended = Nucleus
Scattering Ratefor point-like Nucleus int ρ(r) exp(i q∙r) dV
2
where q = (ki ndash kf) ħ
For elastic scattering at angle θ q = 2p ħ sin(θ2)
Fourier transform of the chargedensity distribution ρ(r)
By measuring the scattering rate at different angles θ and sampling at different valuesof q we can map out the square of the Fourier transform
Then apply an inverse Fourier transform to get the nuclear charge density ρ(r)
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Thus X-ray diffraction image in crystallography gives the squaredFourier transform of the electrondensity inside the crystal
We can do the same thing usingelectron waves to measure thecharge density distributioninside the nucleus
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 13
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- Slide 15
- Slide 16
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- Slide 35
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- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Measure the intensity of the scattered electrons at many values of the angle θto map out the diffraction pattern The width of the diffraction pattern will tellus the size and shape of the nucleus
Now do the same thing with electron waves on a nuclear target
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
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- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Robert Hofstadter1961 Nobel Prizein Physics forwork on elucidatingthe charge distributionof nuclei Mark III electron linear accelerator
at Stanford (up to 1000 MeV energy)
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
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- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
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- Slide 37
- Slide 38
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- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
elastic scattering peaktarget nucleus is leftin its initial state
inelastic scatteringpeaks wherenucleus is leftin an excited state(vibrating or rotating)
443 MeVElectron scattering from 12C nucleus
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
from Krane Introductory Nuclear Physics
diffraction patternof electron waveselasticallyscattering fromnuclei of carbon-12and oxygen-16
Note that carbon-12is smaller so itproduces a widerdiffraction pattern
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
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- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Data for elastic scattering of electronsfrom 208Pb Note that the cross sectionspans 11 orders of magnitude Thismeans that the data at the right handside come in at a rate 1011 more slowlythan the data at the left hand side --a real experimental challenge tomeasure these low cross sections
By measuring the cross sectionextracting the form factor squaredand doing the inverse Fourier transformthe charge distribution of the nucleusis obtained
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
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- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
From the diffraction pattern we can mathematically work backwardsusing an inverse Fourier transform to get the density profile of theelectric charge in the atomic nucleus
Notice how smallthe nucleus is
A Calcium nucleushas a radius ofabout 4 femto-metres)ie 4 x 10-15 metre
while the radius ofa calcium atom hasa radius of
180000 femtometres
ie the nucleus is45000 times smallerin diameter
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Nucleus in an atom is like a pea in a football stadium
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
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- Slide 31
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- Slide 33
- Slide 34
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- Slide 38
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- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
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- Slide 29
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- Slide 31
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- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Even though the atomic nucleus is so tiny compared to the entireatom it contains 9997 of the mass of the atom
The nuclear matter is extremely dense ndash a teaspoon full wouldhave a mass of 460 million metric tons
Where in the universe can we find bulk quantities of nuclear-densitymatter
Answer In neutron stars
A neutron star is formed at the end of the life of a massive starThe pull of gravity is so strong that the protons in the atomic nuclei absorb the orbital electrons forming neutrons Thisallows the whole system to become more compact therebylowering the gravitational potential energy The neutron star is basically a giant nucleus about 25 km in diameter but havinga mass of between 14 and 21 solar masses composed almost exclusively of neutrons
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
2 The nuclear energy scale
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
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- Slide 19
- Slide 20
- Slide 21
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-
Atoms in excited states can de-excite and give off light ofenergies typically around 1 electron-volt
copy Internet Encylopedia of Science wwwdaviddarlinginfoimages
httphyperphysicsphy-astrgsuedu hbasephyoptgratinghtml
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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-
The electrons in atoms (and molecules) are arranged in shellsExcited atoms and molecules are made by boosting the electrons to higher shells
Similarly the protons and neutrons in atomic nuclei are arrangedin shells and excited nuclei are made by boosting the protonsand neutrons to higher shells
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
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- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Why are nuclear energies so high
Because the particles are packed into a very small volume
Using the Heisenberg uncertainty principle
Δp Δx ge h4π
we can calculate the extent Δp that the momentum issmeared out
Since the nucleus is 45000 smaller the momentumof the protons and neutrons is smeared out 45000 timesmore than the electrons in an atom Roughly speakingthe protons and neutrons have 45000 more momentum
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
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- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Recall that kinetic energy KE = frac12 mv2 = p2 2m
and that protons are 1836 times more massive thanelectrons So we get
pnuclear
patomic
= 45000
KEnuclear
KEatomic
= (45000)2 1836 = 11 million
The kinetic energy of protons in the nucleus is about1 million times larger than the kinetic energy ofelectrons in an atom just by the Heisenberg uncertaintyprinciple and in good agreement with experimental data
The high energy of nuclear processes is an inevitable consequenceof the small size of the nucleus + quantum mechanics
This is not so in classical mechanics The kinetic energy of the tinygears in a watch is not much higher than the kinetic energy of theflywheel in a turbine of a hydroelectric generating station
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
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- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
3 The discovery of quarks
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
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- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
By the 1940s it was known that atomic nuclei were made ofprotons and neutrons But do protons and neutrons haveany size Do they have smaller constituents inside of them
Put a liquid hydrogen target into the electron beam and seewhat the diffraction pattern looks like
Recall for a point-like proton with no size we expect this
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
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- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
Stanford Linear Accelerator Centre ndash a 2-mile long electron accelerator which boostselectrons to an energy of 20 billion electron volts (later upgraded to 60)
The de Broglie wavelength of these electrons is about 1100 fm which is about 1the radius of a proton So this machine can resolve features deep inside the proton
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
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- Slide 29
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- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
A view of the gigantic magnetic spectrometer used to analyze theenergy of the scattered electrons Note the two people near the bottom for scale
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
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- Slide 31
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- Slide 42
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- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
each of the peaks correspondsto different scattering processes
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
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- Slide 33
- Slide 34
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- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
-
highest energy scattered electronscorrespond to elastic scattering wherethe electron just bounces off the protonand leaves the proton intact
For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
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For the elastic scattering events the diffraction patterndoes not have a constant intensity The proton is NOTa zero-size point-like particle
These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
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These peaks correspond to inelastic scattering where the target proton is left in an excited state(vibrating rotating) The electron energy is lessbecause it has given up some energy to excitethe proton
The existence of excited states indicates that theproton must have some internal parts that can beboosted up to higher energy levels
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
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- Slide 57
- Slide 58
-
This is the ldquodeep inelastic scatteringrdquo regionwhere the electron has lost a lot of energy whenit scatters from the proton When we plot a graphof the diffraction pattern for these scatteringevents we get the following
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
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- Slide 7
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- Slide 58
-
For the deep inelasticscattering eventswe have a nearlyconstant diffractionpattern
This indicates thatwe are scatteringfrom point-like objects inside theproton These arequarks
(called ldquoscalingrdquo inparticle physics)
This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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This work won the 1990 Nobel Prize in physics forRichard Taylor Henry Kendall and Jerome Friedman
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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