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 1 gram of contaminated ashes[**] were found to have as high as 1,420 decays per second. Suppose that in May 2011, this same 1 gram sample of ashes now has 1,050 decays per second. 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 T_1/2, 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:
  Blank.
  

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: