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:
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):