Physics 6C Summer 2006
Chapter 32 Sample Problems
Chapter 32 Numerical Problems: See the examples worked out the textbook (the sections
that are assigned as reading are listed on the course webpage).
Chapter 32 Conceptual Questions
1.
Nucleus A and nucleus B have different numbers of protons and different numbers of neutrons.
Explain how it is still possible for these nuclei to have equal radii.
Solution: See the back of the textbook.
2. Consider a nucleus that can undergo either (a) α decay or (b) β decay. In each case, state whether
the radius of the resulting daughter nucleus is greater than, less than, or the same as that of the
original nucleus. Explain.
Solution:
(a) The radius of the daughter nucleus is less than that of the original nucleus,
because the radius depends on the number (A) of nucleons according to
r = r0 A1 / 3 , and the daughter nucleus contains four fewer nucleons. (b) The
radius of the daughter nucleus is the same as that of the original nucleus,
because the daughter nucleus contains the same number (A) of nucleons as the
original nucleus.
6. An α particle (charge +2e ) and a β particle (charge −e ) deflect in opposite directions when they
pass through a magnetic field. Which particle deflects by a greater amount, given that both
particles have the same speed? Explain.
Solution:
In general, the amount of deflection is inversely proportional to the radius of
curvature – after all, a large radius implies very little deflection. Recall,
however, that the radius of curvature in a magnetic field (Equation 22-3) is
directly proportional to a particle’s mass and inversely proportional to its
charge. Therefore, the α particle – which has twice the charge but roughly
8000 times the mass – has a larger radius of curvature by a factor of 4000. It
follows that the β particle deflects by the greater amount.
7. Which of the three decay processes (α, β, or γ) results in a new element? Explain.
Solution: See the back of the textbook.
13. The half-life of carbon-14 is 5730 years. Is it possible for any given nucleus in a sample of
carbon-14 to decay after only 1 second has passed? Explain.
Solution: See the back of the textbook.
14. Explain why the large, stable nuclei in Figure 32–1 are found to lie above the N = Z line, rather
than below the line.
Solution:
Above the N = Z line, a nucleus contains more neutrons than protons. This
helps to make the nucleus stable, by spreading out the positive charge of the
protons. If a nucleus were below the N = Z line, it would have more protons
than neutrons, and electrostatic repulsion would blow the nucleus apart.
18. A radioactive sample is placed in a closed container. Two days later only one-quarter of the
sample is still radioactive. What is the half-life of this sample?
Solution:
A radioactive sample will decrease by a factor of two in one half life, and by a
factor of four in two half lives. Therefore, this sample has been in the closed
container for two half lives. It follows that its half life is one day.
19. Radioactive samples A and B have equal half-lives. The initial decay rate R of sample A is twice
that of sample B. What is the ratio of the activity of sample A to that of sample B after two halflives have elapsed?
Solution: See the back of the textbook.
22. The decay rate R is often called the “activity”. The initial activity of sample A is twice that of
sample B. After two half-lives of sample A have elapsed, the two samples have the same activity.
What is the ratio of the half-life of B to the half-life of A?
Solution:
In two half lives, the activity of sample A will be reduced to one-quarter its
initial value. The initial activity of sample B was half that of sample A, but
after two half lives of sample A its activity is now one-quarter the initial
activity of sample A – that is, the two samples have the same activity. It
follows that the activity of sample B decreased by a factor of two in the same
time that the activity of sample A decreased by a factor of four. Therefore,
the half-life of sample B is twice as long as the half-life of sample A.