Physics final exam problem: plutonium-powered pacemaker

Physics 205B Final Exam, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 39.37, Comprehensive Problem 29.79(a)

The energy from the α decay of (238,94)Pu has been used to power cardiac pacemakers, and these plutonium-powered pacemakers need to be properly disposed after being replaced, or removed after a patient dies.[*] In a specific case:
A patient was implanted [in 1978] with a nuclear pacemaker by staff at Lower Bucks Hospital... The pacemaker was [removed] at Nazareth Hospital on October 31, 1996, after the patient had expired... [Later] the pacemaker could not be located and was assumed lost.[**]
(238,94)Pu has a half-life of 88 years. Assume that this plutonium-powered pacemaker still has not been recovered, and is somehow functioning today. Determine the percent decrease in its power output over the past 36 years. Show your work and explain your reasoning.

[*] http://www.orau.org/ptp/collection/miscellaneous/pacemaker.htm.
[**] http://www.nrc.gov/reading-rm/doc-collections/enforcement/actions/materials/ea97005.html.

Solution and grading rubric:
  • p:
    Correct. Finds activity decreases to 75% of its original value, corresponding to a decrease by 25% from its original value.
  • r:
    Nearly correct, but includes minor math errors. Finds activity decreases to 75% 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 25% of its original value, or has calculations nearly set up to find this.
  • 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:
Grading distribution:
Sections 30882, 30883
Exam code: finalEL7a
p: 19 students
r: 1 student
t: 4 students
v: 2 students
x: 5 students
y: 2 students
z: 2 students

A sample "p" response (from student 0618), using the given half-life of 88 years:

Another sample "p" response (from student 3420), converting half-life to decay constant, in order to use the exponential decay equation:

A sample "x" response (from student 0115), at the very least making some sort of educated guesstimate:

A sample "y" response (from student 0003), inexplicably speculating about penguins:

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