Physics final exam problem: Acerinox Cs-137 contamination

Physics 205B Final Exam, spring semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 29.38

In May 1998, the Acerinox steel factory[*] in Spain accidentally recycled material containing radioactive (137,55)Cs, such that contaminated ashes[**] were found to have as high as 1,420 decays per second per gram. Suppose that in May 2011, this same sample of ashes now has 1,050 decays per second per gram. What is the half-life of cesium-137, assuming that it is the only source of radiation in this sample? Show your work and explain your reasoning.

[*] iaea.org/Publications/Booklets/SealedRadioactiveSources/scrap_lessons.html.
[**] www10.antenna.nl/wise/495/4895.html.

Solution and grading rubric:
  • p:
    Correct. Sets up exponential or half-life exponent decay formula to solve for half-life T1/2, given R0 and R, and t = 13 years.
  • r:
    Nearly correct, but includes minor math errors.
  • t:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  • x:
    Implementation of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:

Grading distribution:
Section 30882
Exam code: finalv0L7
p: 3 students
r: 3 students
t: 0 students
v: 1 student
x: 0 students
y: 1 student
z: 0 students

A sample "p" response (from student 2180), using number of radioactive nuclei (N) instead of activity (R), but still essentially correct:

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