Physics quiz question: radioactive decay activity at a later time

Physics 205B Quiz 7, spring semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 29.37

(65,30)Zn has a half-life of 145 days. A sample of this material currently has an activity of 3.20×10⁶ decays/s. The activity of this sample 1.16 days later will be:
(A) 256 decays/s.
(B) 2.76×10³ decays/s.
(C) 1.25×10⁴ decays/s.
(D) 4.00×10⁵ decays/s.

Correct answer (highlight to unhide): (C)

The activity of a sample is given by:

R = R₀·(1/2)^(t/T_1/2),

with R₀, t, and T_1/2 given, then:

R = (3.20×10⁶ decays/s)·(1/2)^{(1.16×103 days/145 days)} = 1.25×10⁴ decays/s.

(Response (A) is (2)^(t/T_1/2); response (B) is R₀/t; response (D) is R₀/8.)

Student responses
Section 31988
(A) : 3 students
(B) : 2 students
(C) : 6 students
(D) : 1 student

Success level: 50%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80