__KING FAHD UNIVERSITY OF PETROLEUM & MINERALS__

**DEPARTMENT OF PHYSICS**

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

**Second Semester 2004 (032)**

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__Homework # 5 __

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**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 ^{131}I(t_{1/2} =
8.0 d) and ^{137}Cs (t_{1/2} = 30 y). There are about five times
as many ^{137}Cs atoms as ^{131}I 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
^{131}I, 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 ^{131}I after 24 h of operation.

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**HW#5P3:
**Krane 6.13

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

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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 ^{14}C 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?