Download Chapter 30: Nuclear Physics

Physics 11 (Fall 2012)
Chapter 30: Nuclear Physics
“You've got a lot of choices. If getting out of bed in the morning is a chore and you're not
smiling on a regular basis, try another choice.” – Steven D. Woodhull
“The greater part of our happiness or misery depends on our dispositions, and not our
circumstances.” – Martha Washington
Reading: pages 991 – 1017
Outline:
⇒ structure of nuclei
atomic number Z and atomic mass number A
isotopes
⇒ nuclear stability (PowerPoint)
strong nuclear force
binding energy
mass defect
⇒ radiation and radioactivity
alpha, beta, and gamma decay
the neutrino (PowerPoint)
⇒ nuclear decay and half-lives
half-life and decay constant
radioactive decay and activity
radioactive carbon dating (read on your own)
⇒ the ultimate building blocks of matter (read on your own)
Problem Solving
Chemical elements are often written with the shorthand notation ZA X where A is the number of
protons plus neutrons, Z is the number of protons, and X is the chemical symbol for the element.
To find the binding energy of a nucleus, use binding energy B = ( Δm )c2 where Δm is the
difference in mass (mass defect) between the nucleus and the mass of the protons plus neutrons.
If masses are given in atomic mass units, then you can use B = ( Δm ) × 931.5 MeV/u.
Some problems deal with the energetics of α and β decays. You should know that a helium
nucleus (two protons and two neutrons) is emitted in an α decay and that either an electron or a
positron is emitted in a β decay. In each case, you should be able to find the resulting nucleus if
the original nucleus is given. You should also be able to calculate the energy released in the
decay if the various masses are given. Recall that the energy released in equal to the binding
energy. If masses are given in atomic mass units, the conversion factor 931.5 MeV/u can be
used.
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Summary
SUMMARY
The goals of Chapter 30 have been to understand the physics of the nucleus and some of the
applications of nuclear physics.
GENERAL PRINCIPLES
The Nucleus
Nuclear Stability
The nucleus is a small, dense, positive core at the center of
an atom.
Proton
Z protons, charge +e, spin 12
N neutrons, charge 0, spin 12
Neutron
The mass number is
A=Z+N
N Low-Z nuclei Line of stability
move closer to
the line of
stability by
beta decay.
Most nuclei are not
stable. Unstable nuclei
undergo radioactive
decay. Stable nuclei
cluster along the line of
stability in a plot of the
isotopes.
Alpha decay is
energetically
favorable for
high-Z nuclei.
Z
Mechanisms by which unstable nuclei decay:
Isotopes of an element have the same
value of Z but different values of N.
The strong force holds nuclei together:
• It acts between any two nucleons.
• It is short range.
Adding neutrons to a nucleus allows the strong force to
overcome the repulsive Coulomb force between protons.
Decay
Particle
Penetration
alpha
beta-minus
beta-plus
gamma
4
low
medium
medium
high
He nucleus
ee+
photon
Alpha and beta decays change the nucleus; the daughter nucleus is a
different element.
The binding energy B of a nucleus depends on the mass
difference between an atom and its constituents:
Alpha decay:
B = (Zm H + Nm n - m atom) * (931.49 MeV/u)
A
ZX
:
A-4
Z-2 Y
Beta-minus decay:
A
ZX
+ a + energy
: Z+1AY + b + energy
IMPORTANT CONCEPTS
Energy levels
Energy
Nucleons fill nuclear energy levels,
similar to filling electron energy
levels in atoms. Nucleons can
often jump to lower energy levels
by emitting beta particles or gamma
photons.
The quark model
12
C
Neutrons
Proton
Nucleons (and other
particles) are made
of quarks. Quarks and
leptons are fundamental
particles.
Protons
d
2
u
1
2
3e
Neutron
d
1
3e
u
1
2
2
3e
Up quark
d
2
1
3e
1
3e
u
1
2
3e
Down quark
APPLICATIONS
Radioactive decay
N = N0 e-t/t
1 t/t1/2
N = N0 a b
2
Measuring radiation
N
The number of undecayed
nuclei decreases exponentially with time t:
The activity of a radioactive sample is the number of decays per second. Activity is related to the half-life as
N0
0.50N0
0.37N0
The half-life
R=
0.693N N
=
t
t1/2
The radiation dose is measured in grays, where
0
0
t1/2
t1/2 = t ln 2 = 0.693t
is the time in which half of any sample decays.
t
t
1 Gy = 1.00 J/kg of absorbed energy
The relative biological effectiveness (RBE) is the biological effect of a
dose relative to the biological effects of x rays. The dose equivalent is
measured in sieverts, where
dose equivalent in Sv = dose in Gy * RBE
Some problems deal with the number and rate of decays. In an original collection of N0 nuclei,
the number that remain undecayed at the end of time t is given by N = N0e-t/τ = N0(½) t/τ . The
time constant τ is related to the half-life t1/2: t1/2 = τ ln2= 0.693τ. The activity is then given by
R = R0e-t/τ = R0(½) t/τ where R0 is the activity at t = 0.
Questions and Example Problems from Chapter 30
Question 1
For each nuclear energy-level diagram in the figure below, state whether it represents a nuclear
ground state, an excited nuclear state, or an impossible nucleus
Question 2
What kind of decay, if any, would you expect for the nuclei with the energy-level diagrams
shown in the figure below?
Problem 1
How many protons and how many neutrons are in (a) 3He, (b) 20Ne, (e) 60Co, and (d) 226Ra?
Problem 2
Mercury 202
80 Hg has an atomic mass of 201.970617 u. Obtain the binding energy per nucleon (in
MeV/nucleon).
Problem 3
Calculate (in MeV) the binding energy per nucleon for 3He and 4He. Which is more tightly bound?
Problem 4
Draw energy-level diagrams. similar to Figure 30.9, for all A = 10 nuclei listed in Appendix D.
Show all the occupied neutron and proton levels. Which of these nuclei do you expect to be
stable?
10
B is a stable nucleus, but 10Be and 10C are radioactive. 10Be undergoes beta-minus decay and
10
C undergoes beta-plus decay. In beta-minus decay, a neutron within the nucleus changes into a
proton and an electron. In beta-plus decay, a proton changes into a neutron and a positron.
Problem 5
For the following nuclei, each undergoing β- decay, write the decay process, identifying each
daughter nucleus, with its chemical symbol and values for Z and A: (a) 146 C and (b) 212
82 Pb
Problem 6
Determine the symbol ZA X for the parent nucleus whose α decay produces the same daughter as
the β- decay of thallium
208
81
Tl .
Problem 7
How many half-lives must elapse until (a) 90% and (b) 99% of a radioactive sample of atoms has
decayed?
Problem 8
The number of radioactive nuclei present at the start of an experiment is 4.60 × 1015. The number
present twenty days later is 8.14 × 1014. What is the half-life (in days) of the nuclei?