atomic physics chapter 28 chapter 28. atomic models
TRANSCRIPT
Atomic Physics
Chapter 28Chapter 28
Atomic Models
Introduction
How do How do neonneon signs work? signs work?
Our main focus will be on the Our main focus will be on the hydrogenhydrogen atom. atom.It is the simplestIt is the simplest
atomic system.atomic system.
Why is it important to study the hydrogen Why is it important to study the hydrogen atom?atom? Studying the quantum numbers for the allowed Studying the quantum numbers for the allowed
states of hydrogen will help us to describe the states of hydrogen will help us to describe the allowed states of allowed states of more complex atomsmore complex atoms. .
The hydrogen atom is an The hydrogen atom is an ideal systemideal system for for relating theory to experimentation.relating theory to experimentation.
Much that we learn about hydrogen can be Much that we learn about hydrogen can be extended to extended to single electron ionssingle electron ions like He and Li. like He and Li.
Early Models Of The Atom
The Greek modelThe Greek model Tiny, hard, indestructible sphereTiny, hard, indestructible sphere
33
The J. J. Thomson modelThe J. J. Thomson model A volume of positive charge is embedded A volume of positive charge is embedded
with negative charges called “electrons”with negative charges called “electrons”
The Rutherford modelThe Rutherford model A positive nucleus orbited by electrons.A positive nucleus orbited by electrons.
The nucleus contains 99.9% of the atom’s The nucleus contains 99.9% of the atom’s massmass
The RutherfordThe Rutherford modelmodel Which force holds the electrons in orbit?Which force holds the electrons in orbit?
The Coulomb forceThe Coulomb force
Problems with the Rutherford Model
There were There were two basic difficultiestwo basic difficulties with with the Rutherford model.the Rutherford model. It could not explain why atoms radiate It could not explain why atoms radiate
discretediscrete frequencies. frequencies. Accelerating electronsAccelerating electrons should radiate should radiate
electromagnetic waves.electromagnetic waves.
Electron Transitions
Using a high voltage to move electrons Using a high voltage to move electrons through a gas causes the gas electrons to through a gas causes the gas electrons to become become excitedexcited and to jump from and to jump from lower lower energy levels to higher energy levelsenergy levels to higher energy levels..
PhotonsPhotons of various wavelengths are of various wavelengths are produced when electrons fall from produced when electrons fall from higher higher energy levels to lower energy levelsenergy levels to lower energy levels..
Emission Spectra
The The emission spectrumemission spectrum of hydrogen of hydrogen Can be produced by applying a high voltage Can be produced by applying a high voltage
across an evacuated glass tube filled with across an evacuated glass tube filled with hydrogen hydrogen
The observed wavelengths are characteristic The observed wavelengths are characteristic only of hydrogenonly of hydrogen
279, 57279, 57
The Balmer Series
In the Balmer SeriesIn the Balmer Series nnff
= 2= 2 There are There are fourfour prominent wavelengths prominent wavelengths
656.3 nm656.3 nm (red)(red)486.1 nm486.1 nm (green)(green)434.1 nm434.1 nm (purple)(purple)410.2 nm410.2 nm (deep violet)(deep violet)
278, 28.7278, 28.7
Balmer Wavelengths
The Balmer Series Wavelength Equation
RRH H is the Rydberg constantis the Rydberg constant
RRH H = 1.0973732 x 10= 1.0973732 x 1077 mm-1-1
€
1
λ= RH
1
22−
1
ni2
⎛
⎝ ⎜
⎞
⎠ ⎟
Two Other Important Series
Lyman seriesLyman series (UV) (UV) nnff
= 1= 1
Paschen seriesPaschen series (IR) (IR) nnff
= 3= 3
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Spectral Lines
How many How many differentdifferent spectral lines spectral lines could be produced by an electron in the could be produced by an electron in the n = 3n = 3 state? state?
ThreeThree
How many How many differentdifferent spectral lines spectral lines could be produced by an electron in the could be produced by an electron in the n = 4n = 4 state? state?
SixSix
Photon Energy
The equation for determining the The equation for determining the energyenergy of the emitted photon in any of the emitted photon in any series:series:
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
2i
2f n
1
n
1eV 13.6E
The Absorption Spectrum
An element can absorb the same An element can absorb the same wavelengths that it emits.wavelengths that it emits.
The spectrum consists of a series of dark The spectrum consists of a series of dark lines.lines.
Identifying Elements
The The absorption spectrumabsorption spectrum was used to was used to identify elements in the solar atmosphere identify elements in the solar atmosphere were identified in this way.were identified in this way.
Helium was discovered.Helium was discovered.
Thermal vs. Atomic Spectra
How could you tell if the light from a How could you tell if the light from a candle flame is candle flame is thermalthermal or or atomicatomic in in origin?origin?
If the spectrum is If the spectrum is continuouscontinuous, the , the source must besource must be thermalthermal..
Auroras
What is the origin of the colors in the What is the origin of the colors in the aurora borealisaurora borealis??
High speed particlesHigh speed particles from space from space interact with the earth’s magnetic field.interact with the earth’s magnetic field.
The Bohr Theory Of Hydrogen
At the beginning of the 20At the beginning of the 20thth century, century, scientists wondered why atoms only scientists wondered why atoms only radiated radiated certain wavelengthscertain wavelengths.. Bohr provided an explanation.Bohr provided an explanation.
Four Assumptions of The Bohr Theory
1) 1) The electron orbits the proton due to theThe electron orbits the proton due to the
Coulomb forceCoulomb force which produces centripetal which produces centripetal
acceleration.acceleration.
2) Only certain electron orbits are 2) Only certain electron orbits are stablestable
and do not radiate energy.and do not radiate energy.
3) 3) RadiationRadiation is only emitted when an is only emitted when an
electron electron dropsdrops from a more energetic from a more energetic
state to a lower state.state to a lower state.
hfEE fi =−
4) 4) The The radiusradius of the electron’s orbit is of the electron’s orbit is
determined by the electron’s determined by the electron’s orbitalorbital
angular momentumangular momentum. .
28.628.6
€
rn = nh
2π mev
⎛
⎝ ⎜
⎞
⎠ ⎟ n = 1, 2, 3, ...
Total Energy of the Hydrogen Atom
The The total energytotal energy of the hydrogen of the hydrogen atom can be determined by using atom can be determined by using this equation.this equation.
€
ET = −k ee
2
2r
The Bohr Radius
An electron can exist only in An electron can exist only in certain certain allowed orbitsallowed orbits determined by the determined by the integer n.integer n.When n = 1, we have what is known When n = 1, we have what is known
as the as the Bohr radiusBohr radius ( (aaoo).).
aaoo = 0.0529 nm = 0.0529 nm
Orbital Radii
A general equation for finding the A general equation for finding the radiusradius of any orbit: of any orbit:
( )Z
2
n
nnm 0.0529r =
Energy States
The The energyenergy for various energy states for various energy states can be found by using:can be found by using:
n= 1 is the ground staten= 1 is the ground state
2
2
n n
ZeV 13.6E −=
Ionization Energy
The minimum energy required to The minimum energy required to ionize the atom is called the ionize the atom is called the ionization energyionization energy..An electron is completely removed An electron is completely removed
from the atom.from the atom.
The Hydrogen Spectrum
The general expression for The general expression for determining wavelengths of the determining wavelengths of the various series in the hydrogen various series in the hydrogen spectrumspectrum
€
1
λ= RH
1
n f2 −
1
ni2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
Bohr’s Correspondence Principle
Quantum mechanicsQuantum mechanics is in agreement is in agreement with with classical physicsclassical physics when the energy when the energy differences between quantized levels differences between quantized levels are very small.are very small.
Successes of the Bohr Theory
It accounted for theIt accounted for the Balmer seriesBalmer series and other and other series.series.
It predicted a value for theIt predicted a value for the Rydberg Rydberg constantconstant that agreed strongly with the that agreed strongly with the experimental value.experimental value.
It gave an expression for theIt gave an expression for the radiusradius of the of the hydrogen atom.hydrogen atom.
It predicted theIt predicted the energy levelsenergy levels of hydrogen.of hydrogen.
It also works with hydrogen-like It also works with hydrogen-like (one (one electron)electron) atoms. atoms. Singly ionized heliumSingly ionized helium
It also works with hydrogen-like It also works with hydrogen-like (one (one electron)electron) atoms. atoms. Doubly ionized lithiumDoubly ionized lithium
It also works with hydrogen-like It also works with hydrogen-like (one (one electron)electron) atoms. atoms. Triply ionized berylliumTriply ionized beryllium
Four Quantum Numbers
The state of an electron is specified byThe state of an electron is specified by fourfour quantum numbers. quantum numbers. These numbers describe These numbers describe allall possible possible
electron states.electron states. The The totaltotal number of electrons in a number of electrons in a
particular energy level is given by:particular energy level is given by:
€
# = 2n2
Principle Quantum Number
The principal quantum numberThe principal quantum number (n) (n) wherewhere n = 1, 2, 3, …n = 1, 2, 3, … Determines the Determines the energyenergy of the allowed of the allowed
states of hydrogenstates of hydrogen States with the same principal quantum States with the same principal quantum
number are said to form a number are said to form a shellshellK, L, M, … (n = 1, 2, 3, …)K, L, M, … (n = 1, 2, 3, …)
Orbital Quantum Number The orbital quantum numberThe orbital quantum number ((ll)) where where ll
ranges from ranges from 00 to to (n – 1)(n – 1) in integral steps in integral steps Allows Allows multiple orbitsmultiple orbits within the same within the same
energy levelenergy level Determines the Determines the shapeshape of the orbits of the orbits States with given values of States with given values of nn and and ll are are
called called subshellssubshellsss ((ll = 0) = 0),, pp ((ll = 1) = 1),, dd ((ll = 2) = 2),, ff ((ll = 3) = 3),, etc… etc…
Electron Subshells
Generally, the electrons in the Generally, the electrons in the ss subshell are subshell are at the lowest energy level and those in the at the lowest energy level and those in the ff subshell in the highest shell occupy the subshell in the highest shell occupy the highest energy level.highest energy level.
As the shell number As the shell number (n)(n) increases the increases the energy difference between the shells energy difference between the shells diminishes, as shown by the decreasing diminishes, as shown by the decreasing distance between each successive shell.distance between each successive shell.
Electron Subshells
Magnetic Quantum Number
The magnetic quantum numberThe magnetic quantum number (m(mll))
wherewhere mmll ranges fromranges from - - ll toto + + ll in in
integral stepsintegral steps Explains why strong magnetic fields can Explains why strong magnetic fields can
cause single cause single spectral linesspectral lines to to splitsplit into into several closely spaced linesseveral closely spaced linesCalled the Zeeman effectCalled the Zeeman effect
Spin Magnetic Quantum Number
The spin magnetic quantum numberThe spin magnetic quantum number (m(mss))
where where mmss can only be can only be + 0.5+ 0.5 or or – 0.5– 0.5 Accounts for the Accounts for the fine structurefine structure of “single” of “single”
spectral lines in the absence of a magnetic fieldspectral lines in the absence of a magnetic field
Hydrogen Like Atoms
Two important equations for Two important equations for hydrogen-likehydrogen-like atoms: atoms: Orbital energyOrbital energy
Orbital radiusOrbital radius
( )eV
n
13.6)ZE
2
2
n −=
€
rn = (0.0529 nm)n2
Z
Angular Momentum
Physicists agreed that angular momentum Physicists agreed that angular momentum was was quantizedquantized but no one was able to but no one was able to explain why.explain why.
28.1028.10
Electron Standing Waves
de Broglie stated that an electron orbit de Broglie stated that an electron orbit would be stable if it contained anwould be stable if it contained an integral numberintegral number of electron of electron wavelengths.wavelengths.
Analogous to Analogous to standing wavesstanding waves in a string in a string
Wave Properties
It became generally agreed upon that It became generally agreed upon that wave propertieswave properties were involved in the were involved in the behavior of atomic systems.behavior of atomic systems.
Quantum Mechanics And The Hydrogen Atom
A review of the various A review of the various quantum number quantum number rangesranges which are used to determine which are used to determine allowable statesallowable states nn can range from can range from 1 1 toto infinity infinity in integral stepsin integral stepsll can range from can range from 0 0 toto (n - 1) (n - 1) in integral stepsin integral steps mmll can range fromcan range from – – ll toto + + ll in integral stepsin integral steps
mmss can only be can only be + ½+ ½ or or – ½– ½
The Spin Magnetic Quantum Number
The spin magnetic quantum number The spin magnetic quantum number explains the explains the splittingsplitting of each energy of each energy level into two level into two (the Zeeman Effect)(the Zeeman Effect).. It explains how two very closely spaced It explains how two very closely spaced
lines may be formed in the spectra of lines may be formed in the spectra of certain gases.certain gases.Electron spin (spin-up and spin-down)Electron spin (spin-up and spin-down)
Questions
2, 8, 122, 8, 12
Pg. 910Pg. 910
Electron Clouds
The electron may be found at various The electron may be found at various distances from the nucleus but the distances from the nucleus but the probability probability of finding it at a distance of finding it at a distance corresponding to the first Bohr orbit is a corresponding to the first Bohr orbit is a maximum.maximum. It can be found in a spherical region known as It can be found in a spherical region known as
thethe ““electron cloudelectron cloud”.”.
281, 282281, 282
The State of an Electron
The The statestate of an electron is specified by of an electron is specified by fourfour quantum numbers. quantum numbers. These numbers describe These numbers describe allall possible possible
electron states.electron states. The The total number of electronstotal number of electrons in a in a
particular energy level is given by:particular energy level is given by:
22n #=
The Pauli Exclusion Principle
Two electrons in an atom can Two electrons in an atom can never never have the same set of quantum numbers.have the same set of quantum numbers. Because of this, the elements all have Because of this, the elements all have
different chemical propertiesdifferent chemical properties.. The The n = 1n = 1 energy level is filled with energy level is filled with
electrons electrons firstfirst..
The Pauli Exclusion Principle And The Periodic Table
MendeleevMendeleev arranged the elements in a arranged the elements in a periodic tableperiodic table according to their atomic according to their atomic masses and chemical similarities.masses and chemical similarities. He left He left gapsgaps which were filled in within the which were filled in within the
next 20 years.next 20 years. Vertical columns have Vertical columns have similar chemical similar chemical
propertiesproperties..
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The Periodic Table
Special Groups Within the Periodic Table
Noble gasesNoble gases The outer shell is The outer shell is filledfilled..
Alkali metalsAlkali metals The outer shell has The outer shell has only one electrononly one electron..
HalogensHalogens The outer shell The outer shell needs one electronneeds one electron..
The Dow Corning Periodic Table
X-Rays
X-rays are X-rays are emittedemitted when a metal target is when a metal target is bombardedbombarded with high-energy electrons to with high-energy electrons to produce:produce: A broad continuous bandA broad continuous band
BremsstrahlungBremsstrahlung Characteristic x-raysCharacteristic x-rays
KK and Kand K
284, 285284, 285
X-Ray Photons
What can the incoming electron from an electron What can the incoming electron from an electron gun do to a gun do to a K-shell electronK-shell electron in a tungsten target in a tungsten target atom?atom? It can knock a It can knock a K-shell electronK-shell electron out of its energy out of its energy
level. Then, an electron from a higher energy level. Then, an electron from a higher energy level can fall into the level can fall into the K-shellK-shell (n = 1).(n = 1).
The energy lost by the falling electron shows The energy lost by the falling electron shows up as an emitted up as an emitted x-ray photonx-ray photon..
Characteristic X-Rays
K-shell emissionK-shell emission produces higher-intensity produces higher-intensity x-rays than Bremsstrahlung.x-rays than Bremsstrahlung.
The x-ray photon comes out at a single The x-ray photon comes out at a single (characteristic)(characteristic) wavelength. wavelength. KK or Kor K
K X-Rays
When an incoming electron forces an When an incoming electron forces an electron out of the K shell electron out of the K shell an electron can an electron can drop down from the drop down from the n = 2n = 2 level and a level and a KK
x-ray photon is emitted.x-ray photon is emitted.
K X-Rays
When an incoming electron forces an When an incoming electron forces an electron out of the K shell electron out of the K shell an electron an electron can drop down from the can drop down from the n = 3n = 3 level and a level and aKK x-ray photon is emitted.x-ray photon is emitted.
Which x-ray photon has the highest energy?Which x-ray photon has the highest energy?
K X-Ray Wavelengths
The wavelength of the emitted The wavelength of the emitted KK
x-ray photon is given by:x-ray photon is given by:
€
1
λ= RH Z −1( )
2 1
12−
1
22
⎛
⎝ ⎜
⎞
⎠ ⎟
Electron Shielding
One electron in the K shell One electron in the K shell partially partially shieldsshields the other from the charge of the the other from the charge of the nucleus. nucleus. Because of this, we use Because of this, we use ZZeffeff = = (Z - 1)(Z - 1)
in the in the KK equation. equation.
K X-Ray Wavelengths
The wavelength of the emitted The wavelength of the emitted KK x- x-
ray photon is given by:ray photon is given by:
€
1
λ= RH Z − 9( )
2 1
12−
1
32
⎛
⎝ ⎜
⎞
⎠ ⎟
Electron Shielding
One electron in the K shell and eight One electron in the K shell and eight electrons in the L shell electrons in the L shell partially shieldpartially shield the M-shell electrons from the charge the M-shell electrons from the charge of the nucleus. of the nucleus. Because of this, we use Because of this, we use ZZeffeff = = (Z - 9)(Z - 9)
in the in the KK equation. equation.
Atomic Transitions
Atoms will only emit or absorb EM Atoms will only emit or absorb EM radiation at certain frequencies radiation at certain frequencies corresponding to corresponding to transitionstransitions involving involving the various energy states.the various energy states.
Stimulated Absorption
In the In the stimulated absorptionstimulated absorption process, process, light may be used to light may be used to stimulate stimulate electronselectrons to higher excited states. to higher excited states. Only certain frequencies will do this.Only certain frequencies will do this.
28.1728.17
Spontaneous Emission
When the electrons When the electrons randomlyrandomly fall back fall back to their original orbits we call this to their original orbits we call this spontaneous emissionspontaneous emission..
286286
Spontaneous Emission
Stimulated Emission
In In stimulated emissionstimulated emission, all of the , all of the electrons can be made to fall back electrons can be made to fall back at at the same timethe same time and thus produce bright, and thus produce bright, coherent light.coherent light. This is the basis for the operation of This is the basis for the operation of
LASERSLASERS..
Stimulated Emission
Lasers
LASERLASER - - LLightight AAmplification bymplification by SStimulatedtimulated EEmission ofmission of RRadiationadiation
Population Inversion
In a laser, electrons are stimulated so In a laser, electrons are stimulated so that there arethat there are more electrons in the more electrons in the excited stateexcited state than in the ground state.than in the ground state. This is called a This is called a population inversionpopulation inversion..
287287
Laser Requirements
There are There are three conditionsthree conditions for laser for laser action to occur.action to occur. A population inversionA population inversion The excited state must be a metastable The excited state must be a metastable
(long lifetime)(long lifetime) state. state. The photons must be confined long The photons must be confined long
enough to stimulate further emissions.enough to stimulate further emissions.
He-Ne Lasers
The operation of a The operation of a He-NeHe-Ne laser laser An oscillator is used to sweep electrons through An oscillator is used to sweep electrons through
a thin glass tube containing a a thin glass tube containing a He-Ne mixtureHe-Ne mixture.. The neon atoms are raised to a The neon atoms are raised to a metastablemetastable state state
by collisions with excited helium atoms.by collisions with excited helium atoms. Electrons simultaneously returning to a lower Electrons simultaneously returning to a lower
energy state emit energy state emit coherent photonscoherent photons of a of a particular wavelength. particular wavelength. (632.8 nm)(632.8 nm)
28.22a, 71, 28828.22a, 71, 288
Laser Frequencies
Frequency ranges of lasersFrequency ranges of lasers InfraredInfrared (CO (CO22)) VisibleVisible ( (redred, , greengreen, , blueblue)) UltravioletUltraviolet
Laser Applications
MedicalMedical ““Welding” detached retinasWelding” detached retinas Laser surgeryLaser surgery Laser vision correction (Lasik)Laser vision correction (Lasik)
Lasik Surgery
An ultra-thin flap is created on the eye's surface An ultra-thin flap is created on the eye's surface during LASIK corrective eye surgery. After laser during LASIK corrective eye surgery. After laser energy is applied to reshape the eye, the flap is energy is applied to reshape the eye, the flap is replaced to serve as a type of natural bandage.replaced to serve as a type of natural bandage.
Surveying and distance measurementSurveying and distance measurement
Cutting and drilling metals in industryCutting and drilling metals in industry
Fiber optic communicationsFiber optic communications
Holography
Used in the production of Used in the production of three-dimensional three-dimensional imagesimages
Interference patternsInterference patterns are placed on film. are placed on film. Used to protect Used to protect credit cardscredit cards
283, 284283, 284
Making Holograms
CDs and DVDs
Information is stored in Information is stored in binarybinary form. form. Pits and land areas (ones and zeros)Pits and land areas (ones and zeros)
The laser beam follows a The laser beam follows a spiral pathspiral path.. A A diffraction gratingdiffraction grating is used to provide is used to provide
tracking.tracking. 40+ second memory40+ second memory for music CDs for music CDs
Infrared Remote Control
A different A different infraredinfrared wavelength is assigned to wavelength is assigned to each number or function.each number or function. TV and stereo remote controls use IR.TV and stereo remote controls use IR. Some computers and calculators use IR. Some computers and calculators use IR. My MAC PowerPoint remote uses RF.My MAC PowerPoint remote uses RF.
Don’t confuse Don’t confuse IRIR with with RFRF controls. controls. MAC Photo Booth DemoMAC Photo Booth Demo
Semiconductor Devices
DopingDoping Donor atomsDonor atoms N-type semiconductorN-type semiconductor Acceptor atomsAcceptor atoms P-type semiconductorsP-type semiconductors
Semiconductor Devices
P-N junctionsP-N junctions DiodesDiodes
Forward biasForward biasReverse biasReverse bias
Half-wave rectifiersHalf-wave rectifiers Full-wave rectifiersFull-wave rectifiers TransistorsTransistors
Transistors
Junction transistorsJunction transistors TypesTypes
npn npn pnppnp
Parts of a transistorParts of a transistorEmitterEmitterBaseBaseCollectorCollector
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Semiconductor Devices
Integrated circuitsIntegrated circuits What are they?What are they? Where are they used?Where are they used? What are the advantages of integrated What are the advantages of integrated
circuits?circuits?
Computer Memory
Questions
7, 9 - 11, 157, 9 - 11, 15
Pg. 910Pg. 910