20180423

Physics quiz question: half-life of Cs-137

Physics 205B Quiz 7, spring semester 2014
Cuesta College, San Luis Obispo, CA

A medical radiotherapy source was stolen in Goiânia, Brazil, releasing radioactive contamination resulting in four deaths and 249 survivors before most of its contents was recovered. Over 25 years, the activity of the unrecovered portion of the source still in the environment has decreased from an estimated 7.0×1012 decays/second to 3.9×1012 decays/second. The half-life of this material is:
(A) 10 years.
(B) 14 years.
(C) 30 years.
(D) 36 years.

[*] wki.pe/Goi%C3%A2nia_accident.

Correct answer (highlight to unhide): (C)

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 T1/2 using the time t = 25 years that it took for the activity to drop down from R0 = 7.0×1012 decays/second down to R = 3.9×1012 decays/second, then:

(R/R0) = (1/2)(t/T1/2);

ln(R/R0) = (t/T1/2)·ln(1/2);

T1/2 = t·ln(1/2)/ln(R/R0);

T1/2 = (25 years)·ln(1/2)/(ln((3.9×1012 decays/second)/(7.0×1012 decays/second)) = 29.6250371579... years,

or to two significant figures, the half-life of this sample is 30 years.

(Response (A) is t·ln(R/R0)·ln(1/2); response (B) is t·(R/R0); response (D) is –t/ln(1/2).)

Student responses
Sections 30882, 30883
Exam code: quiz07bC4n
(No responses recorded.)