ib assessment statements topic 13.2, nuclear physics 13.2.1.explain how the radii of nuclei may be...
TRANSCRIPT
DEVIL PHYSICSTHE BADDEST CLASS ON
CAMPUSIB PHYSICS
TSOKOS LESSON 6-6NUCLEAR PHYSICS
IB Assessment Statements
Topic 13.2, Nuclear Physics13.2.1. Explain how the radii of nuclei
may be estimated from charged particle scattering experiments.
13.2.2. Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer.
13.2.3. Describe one piece of evidence for the existence of nuclear energy levels.
IB Assessment Statements
Topic 13.2, Nuclear Physics13.2.4. Describe β+ decay, including
the existence of the neutrino.13.2.5. State the radioactive decay
law as an exponential function and define the decay constant.
13.2.6. Derive the relationship between decay constant and half-life.
IB Assessment Statements
Topic 13.2, Nuclear Physics13.2.7. Outline methods for
measuring the half-life of an isotope.
13.2.8. Solve problems involving radioactive half-life.
Objectives
Solve problems of closest approach using the law of conservation of energy and appreciate that nuclei have well-defined radii
Describe a mass spectrometer and its implications for isotope existence
State theoretical arguments that have been used to postulate the existence of the neutrino
Objectives
State the radioactive decay law,
State the meaning of half-life and decay constant and derive the relationship between them
t
t
eNdt
dNA
eNN
)( 0
0
Objectives
Appreciate that the decay constant is the probability of decay per unit time
Understand that the initial activity of a sample is,
Obtain short and long half-lives from experimental data
0NA
Objectives
Solve problems with activities and the radioactive decay law
Scattering Experiments and Distance of Closest Approach An alpha particle of charge q=+2e is
fired head-on at a nucleus The particle’s total energy is kinetic,
E=Ek
Scattering Experiments and Distance of Closest Approach The particle is repelled by the
positive charge of the nucleus
Scattering Experiments and Distance of Closest Approach When the particle stops, all of its
kinetic energy has been converted into potential energy
d
ZekE
d
eZekE
d
QqkE
22
2
Scattering Experiments and Distance of Closest Approach When the particle stops, all of its
kinetic energy has been converted into potential energy
K
K
E
Zekd
d
ZekE
2
2
2
2
Scattering Experiments and Distance of Closest Approach As kinetic energy of the alpha
particle increases, distance decreases until the nuclear radius is reached
K
K
E
Zekd
d
ZekE
2
2
2
2
Scattering Experiments and Distance of Closest Approach Rutherford Scattering
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
Closest Approach to Nucleus http://hyperphysics.phy-astr.gsu.edu/hbase/h
frame.html Nuclear Radius Relationship
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
Scattering Experiments and Distance of Closest Approach Further experiments have been able
to refine the estimates for nuclear radii to be
mxxAR 1531 102.1
Mass Spectrometer
B
Ev
evBeE
Positive ions pass through a combination magnetic and electric field so that only ones with a certain velocity will pass through S2
Mass Spectrometer
v
eBRm
eB
mvR
evB
mvR
R
vmevBF
2
2 The positive ions then enter a third magnetic field which causes the ion to take a circular path, the radius of which is determined by its mass.
Mass Spectrometer Given the same
velocity, particles with a greater mass will have greater kinetic energy and thus a larger radius of curvature
Existence of isotopes was found using a mass spectrometer
Beta Decay and the Neutrino Decay of a neutron
Decays into a proton, electron, and an antineutrino
This happens to free neutrons outside the nucleus because neutrons have greater mass than protons
Half-life is about 11 minutes
evepn 00
01
11
10
Beta Decay and the Neutrino Decay of a proton
Decays into a neutron with the emission of a positron (anti-particle of an electron) and a neutrino
Decay occurs inside the nucleus where binding energy makes up for the mass difference
Not a split, but a disappearance and reformation
evenp 00
01
10
11
Beta Decay and the Neutrino Presence of neutrinos
predicted because the mass of a neutron is greater than the sum of the mass of a proton and electron
evepn 00
01
11
10
evenp 00
01
10
11
Beta Decay and the Neutrino In other decays, this
mass difference showed up in kinetic energy of the particles
evepn 00
01
11
10
evenp 00
01
10
11
Beta Decay and the Neutrino Absence of the kinetic
energy led to experiments that uncovered the neutrino (little neutral one) in 1953
evepn 00
01
11
10
evenp 00
01
10
11
Beta Decay and the Neutrino Electron Capture
A proton inside the nucleus captures an electron and turns into a neutron and neutrino
This is the process occurring in neutron stars
Huge pressure inside the star drives electrons into protons, turning them into neutrons
evnep 00
10
01
11
Beta Decay and the Neutrino Examples of Beta
Decayevepn 0
001
11
10 evenp 0
001
10
11 evnep 0
010
01
11
Nuclear Energy Levels
The nucleus, like the atom, exists in discrete energy levels
Main evidence is that alpha particles and gamma ray photons are emitted in discrete energy levels during decays
In beta decays, the electrons have a continuous range of energies
Nuclear Energy Levels
Nuclear energy levels of
Shown is a gamma decay (release of a photon) with energy
Mg2412
MeV87.337.124.5
Nuclear Energy Levels
Two decays of plutonium into uranium with release of an alpha particle
4223892
24294 UPu
Radioactive Decay Law
The number of nuclei that will decay per second is proportional to the number of atoms present that have not yet decayed
λ is a constant known as the decay constant
Represents the probability of decay per unit time
Ndt
dN
Radioactive Decay Law
The number of undecayed nuclei N at any given time in relation to the original number of undecayed nuclei N0 is given by the equation,
The decay rate is exponential
teNN 0
Radioactive Decay Law
The derivation to the right gives the relationship between half-life and decay rate
2/1
00
0
693.0
ln2
1ln
2
2/1
2/1
T
e
eNN
eNN
T
T
t
Radioactive Decay Law
Radioactive Decay Law
The number of decays per second is called the activity,
The initial activity is
00
0
0
NA
eNA
dt
dNA
eNN
t
t
Radioactive Decay Law
The decay constant represents the probability of decay per unit time
dt
yprobabilit
dtN
dNyprobabilit
NdtdN
Ndt
dN
Σary Review
Can you solve problems of closest approach using the law of conservation of energy and appreciate that nuclei have well-defined radii?
Can you describe a mass spectrometer and its implications for isotope existence?
Can you state theoretical arguments that have been used to postulate the existence of the neutrino?
Σary Review
Can you state the radioactive decay law,
? Can you state the meaning of half-life
and decay constant and derive the relationship between them?
t
t
eNdt
dNA
eNN
)( 0
0
Σary Review
Do you appreciate that the decay constant is the probability of decay per unit time?
Do you understand that the initial activity of a sample is,
? Can you obtain short and long half-
lives from experimental data?
0NA
Σary Review
Can you solve problems with activities and the radioactive decay law?
IB Assessment Statements
Topic 13.2, Nuclear Physics13.2.1. Explain how the radii of nuclei
may be estimated from charged particle scattering experiments.
13.2.2. Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer.
13.2.3. Describe one piece of evidence for the existence of nuclear energy levels.
IB Assessment Statements
Topic 13.2, Nuclear Physics13.2.4. Describe β+ decay, including
the existence of the neutrino.13.2.5. State the radioactive decay
law as an exponential function and define the decay constant.
13.2.6. Derive the relationship between decay constant and half-life.
IB Assessment Statements
Topic 13.2, Nuclear Physics13.2.7. Outline methods for
measuring the half-life of an isotope.
13.2.8. Solve problems involving radioactive half-life.
QUESTIONS?
HOMEWORK#1-20