KING FAHD UNIVERSITY OF PETROLEUM & MINERALS

DEPARTMENT OF PHYSICS

PHYS 422 Nuclear and Particle Physics (3-0-3)

Second Semester 2004 (032)

Homework # 5  

HW#5P1: Krane 6.1

Three radioactive sources each have activities of 1.0  at t = 0. Their half-lives are, respectively, 1.0 s, 1.0 h, and 1.0 d. (a)  How many radioactive nuclei are present at t = 0 in each source?  (b)  How many nuclei of each source decay between t = 0 and t = 1 s? (c) How many decay between t = 0 and t = 1 h?

HW#5P2: Krane 6.3

Among the radioactive products emitted in the 1986 Chernobyl reactor accident were ¹³¹I(t_1/2 = 8.0 d) and ¹³⁷Cs (t_1/2 = 30 y). There are about five times as many ¹³⁷Cs atoms as ¹³¹I atoms produced in fission.  (a)  Which isotope contributes the greater activity to the radiation cloud? Assume the reactor had been operating continuously for several days before the radiation was released.  (b)  How long after the original incident does it take for the two activities to become equal?  (c)  About 1% of fission events produce ¹³¹I, and each fission event releases an energy of about 200 MeV. Given a reactor of the Chernobyl size (1000 MW), calculate the activity in curies of ¹³¹I after 24 h of operation.

HW#5P3: Krane 6.13

The decay chain is observed  from an initially pure sample of 1 mCi of ¹³⁹Cs. The half lives are ¹³⁹Cs, 9.5 min; ¹³⁹Ba, 82.9 min; ¹³⁹La, stable. What is the maximum ¹³⁹Ba activity and when does it occur?

HW#5P4: Krane 6.18

            It is desired to determine the age of a wood timber used to construt an ancient shelter. A sample of the wood is analyzed for its ¹⁴C content and gives 2.1 decays per minute. Another sample of the same size from a recently cut tree of the same type gives 5.3 decays per minute. What is the age of the sample?