Physics final exam problem: radioactive age of sample

Physics 205B Final Exam, Fall Semester 2010
Cuesta College, San Luis Obispo, CA

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

[20 points.] A sample is melted, and is found to contain 1.707 g of potassium-40 and 1.445 g of argon-40. Assume that potassium-40 can only decay to argon-40 with a half-life of 1.248e9 years. If the sample originally contained no argon-40, how old is it? Show your work and explain your reasoning.

Solution and grading rubric:
  • p = 20/20:
    Correct. Sets up exponential or half-life exponent decay formula to solve for t, given N_0 and N (converted from g to moles), and T_(1/2).
  • r = 16/20:
    Nearly correct, but includes minor math errors.
  • t = 12/20:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
  • v = 8/20:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  • x = 4/20:
    Implementation of ideas, but credit given for effort rather than merit.
  • y = 2/20:
    Irrelevant discussion/effectively blank.
  • z = 0/20:

Grading distribution:
Section 31988
p: 1 student
r: 3 students
t: 1 student
v: 5 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 2051):

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