Question

A radioactive sample $S_1$ having the activity $A _1$ has twice the number of nuclei as another sample $S_2$ of activity $A_2$ If $A_2 = 2A_1$ then the ratio of half life of $S_1$ to the half life of $S_2$ is

• A. $0.25$
• B. $0.75$
• C. $4$
• D. $2$

Answer 1

Answer: (C)

Activity, $A=\lambda N=\frac{0.693}{T_{1 / 2}} N$
where $T_{1 / 2}$ is the half-life of a radioactive sample.
$\therefore \frac{A_{1}}{A_{2}} =\frac{N_{1}}{T_{1}} \times \frac{T_{2}}{N_{2}}$
$\frac{T_{1}}{T_{2}} =\frac{A_{2}}{A_{1}} \times \frac{N_{1}}{N_{2}}$
$=\frac{2 A_{1}}{A_{1}} \times \frac{2 N_{2}}{N_{2}}=\frac{4}{1}$