Transcript File - SPHS Devil Physics

DEVIL PHYSICS
THE BADDEST CLASS ON CAMPUS
IB PHYSICS
TSOKOS LESSON 6-6
NUCLEAR PHYSICS
IB Assessment Statements
Topic 13.2, Nuclear Physics
13.2.1. 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 Physics
13.2.4. 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 Physics
13.2.7. Outline methods for measuring the halflife 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,
N  N 0 e  t
dN
A
 ( N 0  ) e  t
dt
 State the meaning of half-life and decay
constant and derive the relationship between
them
Objectives
 Appreciate that the decay constant is the
probability of decay per unit time
 Understand that the initial activity of a
sample is,
A  N 0
 Obtain short and long half-lives from
experimental data
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
Qq
Ek
d

Ze 2e 
Ek
d
2
2 Ze
Ek
d
Scattering Experiments and
Distance of Closest Approach
 When the particle stops, all of its kinetic
energy has been converted into potential
energy
2Ze
EK  k
d
2
2Ze
d k
EK
2
Scattering Experiments and
Distance of Closest Approach
 As kinetic energy of the alpha particle
increases, distance decreases until the
nuclear radius is reached
2Ze
EK  k
d
2
2Ze
d k
EK
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/hframe.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
15
R  1.2 xA x10 m
13
Mass Spectrometer
eE  evB
E
v
B
Positive ions pass through a
combination magnetic and
electric field so that only ones
with a certain velocity will pass
through S2
Mass Spectrometer
2
v
F  evB  m
R
m v2
R
evB
mv
R
eB
R eB 
m
v
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
1
0
n p e v
1
1
0
1
0
0 e
 This happens to free neutrons outside the nucleus
because neutrons have greater mass than protons
 Half-life is about 11 minutes
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
1
1
p n e v
1
0
0
1
0
0 e
 Decay occurs inside the nucleus where binding
energy makes up for the mass difference
 Not a split, but a disappearance and reformation
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
1
0
n p e v
1
1
p n e v
1
1
1
0
0
1
0
1
0
0 e
0
0 e
Beta Decay and the Neutrino
 In other decays, this mass
difference showed up in
kinetic energy of the
particles
1
0
n p e v
1
1
p n e v
1
1
1
0
0
1
0
1
0
0 e
0
0 e
Beta Decay and the Neutrino
 Absence of the kinetic
energy led to experiments
that uncovered the
neutrino (little neutral one)
in 1953
1
0
n p e v
1
1
p n e v
1
1
1
0
0
1
0
1
0
0 e
0
0 e
Beta Decay and the Neutrino
 Electron Capture
 A proton inside the nucleus captures an electron
and turns into a neutron and neutrino
1
1
p e n v
0
1
1
0
0
0 e
 This is the process occurring in neutron stars
 Huge pressure inside the star drives electrons into
protons, turning them into neutrons
Beta Decay and the Neutrino
 Examples of Beta Decay
1
0
n p e v
1
1
0
1
0
0 e
1
1
p n e v
1
0
0
1
0
1
0 e 1
p e n v
0
1
1
0
0
0 e
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
24
12
Mg
 Shown is a gamma decay
(release of a photon) with
energy
5.24  1.37  3.87 MeV
Nuclear Energy Levels
 Two decays of
plutonium into uranium
with release of an alpha
particle
242
94
Pu U  
238
92
4
2
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
dN
 N
dt
 λ is a constant known as the decay constant
 Represents the probability of decay per unit
time
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,
N  N0 e
t
 The decay rate is exponential
Radioactive Decay Law
N  N 0e
 The derivation to the
right gives the
relationship between
half-life and decay rate
 t
N0
 T1 / 2
 N 0e
2
1
 T1 / 2
ln  ln e
2
0.693  T1/ 2


Radioactive Decay Law
Radioactive Decay Law
 The number of decays per
second is called the
activity,
 The initial activity is
N  N 0e
 t
dN
A
dt
 t
A   N 0  e
A0  N 0 
Radioactive Decay Law
 The decay
constant
represents the
probability of
decay per unit
time
dN
  N
dt
dN  Ndt
dN
probability 
 dt
N
probability

dt
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,
N  N 0 e  t
dN
A
 ( N 0  ) e  t
dt
?
 Can you state the meaning of half-life and
decay constant and derive the relationship
between them?
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,
A  N 0
?
 Can you obtain short and long half-lives from
experimental data?
Σary Review
 Can you solve problems with activities and
the radioactive decay law?
IB Assessment Statements
Topic 13.2, Nuclear Physics
13.2.1. 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 Physics
13.2.4. 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 Physics
13.2.7. Outline methods for measuring the halflife of an isotope.
13.2.8. Solve problems involving radioactive
half-life.
QUESTIONS?
HOMEWORK
#1-20