Physics final exam problem: initial activity of radioactive sample

Physics 205B Final Exam, spring semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 29.34

A commercially available sample from a medical supply company contains the isotope phosphorus-32, which undergoes β– decay with a half-life of 14.3 days. As listed on the company's website[*], new samples are prepared every Thursday. When a sample arrives on Monday morning (four days later), a Physics 205B student finds that it has an activity of 1.52×10⁷ decays/s. Determine the initial activity of this sample when it was first prepared. Show your work and explain your reasoning.

[*] las.perkinelmer.com/Catalog/ProductInfoPage.htm?ProductID=NEG502H500UC.

Solution and grading rubric:

• p:
  Correct. Sets up exponential or half-life exponent decay formula to solve for R₀, given R, t, and T_1/2).
  
• 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 31988
p: 3 students
r: 6 students
t: 0 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1448) using the half-life decay formula:

A sample "p" response (from student 4747) using the exponential decay formula:

A sample "v" response (from student 7676):