Question

The half-life of cobalt-60 is 5.25 yrs. After how long does its activity reduce to about one eight of its original value?

• A. 5.25 years
• B. 10.50 years
• C. 15.75 years
• D. 21 years

Answer 1

The correct option is C

15.75 years

The activity is proportional to the number of undecayed atoms: In each half-life, the remaining sample decays to half of its initial value. Since $\left(\frac{1}{2}\right)\times \left(\frac{1}{2}\right)\times \left(\frac{1}{2}\right)=\frac{1}{8}$, therefore, three half-lives or 15.75 years are required for the sample to decay to $\frac{1}{8}$th its original strength.