Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 39.37, Comprehensive Problem 29.79(a)
The following posts were made on an online discussion board[*]:
LZ: Well from what I've been told, the tritium tubes in a Marathon watch[**] last up to 20 years...Assume that the brightness of a tritium-powered watch is proportional to the activity. Determine the percent decrease in brightness of a tritium-powered watch in 20 years. Show your work and explain your reasoning.
sharp: The "lasts for 20 years" is a misnomer. Tritium has a half-life of 12.3 years, which means that 12.3 years after a set amount of tritium is created, half of its radioactivity will be gone: half its brightness. It doesn't mean in 20 years the light will just turn off, but that some marketing guy thinks that in 20 years the brightness will be too dim to be usable (or long after the watch falls apart).
[*] "Tritium Watches / Pros and Cons," edcforums.com/threads/tritium-watches-pros-and-cons.48729/.
[**] topspecus.com/shop/category/marathon-watches/.
Solution and grading rubric:
- p:
Correct. Finds activity decreases to 32% of its original value, corresponding to a decrease by 68% from its original value. - r:
Nearly correct, but includes minor math errors. Finds activity decreases to 32% of its original value, but garbles the percent decrease by calculation. - t:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Only has activity decreasing to 32% of its original value. - 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.
Sections 30882
Exam code: finalpL3x
p: 13 students
r: 1 student
t: 4 students
v: 7 students
x: 2 students
y: 1 student
z: 2 students
A sample "p" response (from student 2121), using the half-life decay equation:
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