Physics 205B Quiz 7, spring semester 2017
Cuesta College, San Luis Obispo, CA
Bi(209,83) has the longest known half-life of any isotope that undergoes alpha decay, with a half-life of 1.9×10
19 years[*].
It will take __________ for a sample of Bi(209,83) to decrease its activity by 1.0%.
(A) 1.9×10
17 years.
(B) 2.8×10
17 years.
(C) 2.7×10
19 years.
(D) 3.8×10
19 years.
[*] Pierre de Marcillac, Noël Coron, Gérard Dambier, Jacques Leblanc and Jean-Pierre Moalic, "Experimental Detection of α-Particles from the Radioactive Decay of Natural Bismuth,"
Nature, vol. 422 (April 24, 2003),
pp. 876-878
nature.com/nature/journal/v422/n6934/full/nature01541.html.
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 time
t it would take for the activity to drop down to
R = 0.990 (assuming
R0 started at exactly 1, as it "decreases its activity by 1.0%" down to 99.0%), then:
(
R/
R0) = (1/2)
(t/T1/2);
ln(
R/
R0) = (
t/
T1/2)·ln(1/2);
t =
T1/2·ln(
R/
R0)/ln(1/2);
t = (1.9×10
19 years)·(ln(0.990/1)/ln(1/2) = 2.754918242×10
17 years,
or to two significant figures, it will take this sample 2.8×10
17 years to decrease its activity by 1.0%.
(Response (A) is 1% of
T1/2; response (C) is the time constant τ = 1/(
T1/2·ln(2)); response (D) is the time it would take for the sample to decrease its activity by 99% (or decrease its activity down to 1%.)
Sections 30882, 30883
Exam code: quiz07N4ci
(A) : 12 students
(B) : 7 students
(C) : 5 students
(D) : 2 students
Success level: 27%
Discrimination index (
Aubrecht & Aubrecht, 1983): 0.57