HW3 (Due, March 31, 2015) 1. The activity of a radioisotope is found

ATOM AND RADIATION PHYSICS
HW3 (Due, March 31, 2015)
1. The activity of a radioisotope is found to decrease by 30% in 1 wk. What are the values of
its
(a) decay constant
(b) half-life
(c) mean life?
2. A very old specimen of wood contained 1012 atoms of 14C in1986.
(a) How many 14C atoms did it contain in the year 9474 B.C.?
(b) How many 14C atoms did it contain in 1986 B.C.?
3. 136Cs (half-life = 13.7 d) decays (β–) into
stable 136Ba:
136m
Ba (half-life = 0.4 s), which decays (γ ) into
(a) Calculate the decay constant of 136Cs.
(b) Calculate the specific activity of 136Cs.
(c) Starting with a pure 1010-Bq sample of 136Cs at time t = 0, how many atoms of
decay between time t1 = 13.7 d (exactly) and time t2 = 13.7 d + 5 s (exactly)?
136m
Ba
4. A 6.2-mg sample of 90Sr is in secular equilibrium with its daughter 90Y.
(a) How many Bq of 90Sr are present?
(b) How many Bq of 90Y are present?
(c) What is the mass of 90Y present?
(d) What will the activity of the 90Y be after 100 y?
5. A room measures 10 m×8 m×3 m. It contains 80 pCi L–1 of 218Po, 60 pCiL–1 of 214Pb, and
25 pCi L–1 each of 214Bi and 214Po.
(a) Calculate the WL concentration in the room.
(b) Calculate the total potential alpha-particle energy in the room.
(c) What is the concentration of 214Po atoms in the air?
(d) If secular equilibrium existed at this working-level concentration, what would be the
activity concentration of 214Pb atoms?
(e) What would be the exposure in WLM of an individual who occupied the room 12 hours
per day, 6 days per week, for one year?
6. (a) Calculate the maximum energy that a 3-MeV alpha particle can transfer to an electron
in a single collision.
(b) Repeat for a 100-MeV pion.
7. If the macroscopic cross section for a charged particle is 62 μm–1, what is the average
distance of travel before having a collision?
8. Compute the mean excitation energy of (a) Be, (b) Al, (c) Cu, (d) Pb.
9. (a) Use Table 5.2 to determine F(β) for a 5-MeV deuteron.
(b) What is the stopping power of water for a 5-MeV deuteron?
10. Using Eq. (5.37), calculate the stopping power of water for
(a) a 7-MeV proton,
(b) a 7-MeV pion,
(c) a 7-MeV alpha particle.
Compare answers with Fig. 5.6.
11. 239Pu emits a 5.16-MeV alpha particle. What is its range in cm in
(a) muscle,
(b) bone of density 1.9 g cm–3,
(c) air at 22◦C and 750 mm Hg?
12. (a) Estimate the slowing-down time for a 2-MeV pion in water.
(b) Repeat for a 2-MeV muon.
(c) Give a physical reason for the difference in the times.