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 T1/2). - 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):
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