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 7.0×10

^{12}decays/second to 3.9×10

^{12}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*=

*R*

_{0}·(1/2)

^{(t/T1/2)},

where

*T*

_{1/2}is the half-life. Solving for the

*T*

_{1/2}using the time

*t*= 25 years that it took for the activity to drop down from

*R*

_{0}= 7.0×10

^{12}decays/second down to

*R*= 3.9×10

^{12}decays/second, then:

(

*R*/

*R*

_{0}) = (1/2)

^{(t/T1/2)};

ln(

*R*/

*R*

_{0}) = (

*t*/

*T*

_{1/2})·ln(1/2);

*T*

_{1/2}=

*t*·ln(1/2)/ln(

*R*/

*R*

_{0});

*T*

_{1/2}= (25 years)·ln(1/2)/(ln((3.9×10

^{12}

^{12}

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

(Response (A) is

*t*·ln(

*R*/

*R*

_{0})·ln(1/2); response (B) is

*t*·(

*R*/

*R*

_{0}); response (D) is –

*t*/ln(1/2).)

Student responses

Sections 30882, 30883

Exam code: quiz07bC4n

(No responses recorded.)