20120512

Physics quiz question: percent decrease in radioactivity

Physics 205B Quiz 7, spring semester 2012
Cuesta College, San Luis Obispo, CA

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

"Artist concept of NASA's Voyager spacecraft"
NASA/JPL-Caltech
nasa.gov/mission_pages/voyager/voyager20120117.html

Radioactive (238,94)Pu, used in the radioisotope thermoelectric generator (RTG) power source for NASA's Voyager 1 spacecraft, undergoes α decay with a half-life of 87.7 years. The RTG power source aboard Voyager 1 is expected to allow operations to continue for at least 50 years after its launch[*]. What is the percent decrease in activity for the (238,94)Pu during this time?
(A) 1.3%.
(B) 33%.
(C) 43%.
(D) 57%.

[*] en.wikipedia.org/wiki/Voyager_1#Power.

Correct answer (highlight to unhide): (B)

The activity of a sample is given by:

R = R0·(1/2)(t/T1/2),

where T1/2 is the half-life. Solving for the activity at t = 50 years, assuming that R0 will be normalized to 1:

(R/R0) = (1/2)(t/T1/2) = (1/2)(50 years/87.7 years) = 0.67,

So the percent decrease in 30 minutes will be 1 – 0.67 = 0.33, or 33%.

(Response (A) is the time constant τ = 1/(T1/2·ln(2)) divided by 100; response (C) is exp(–50/87.7), and response (D) is 1 – exp(–50/87.7), presumably confusing T1/2 with τ in the exponential decay formula.)

Section 30882
Exam code: quiz07b3Ta
(A) : 2 students
(B) : 11 students
(C) : 3 students
(D) : 9 students

"Success level": 44%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.38

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