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.
$\therefore \frac{A_1}{A_2}=\frac{N_1}{T_1}\times \frac{T_2}{N_2}$
$\frac{T_1}{T_2}=\frac{A_2}{A_1}\times \frac{N_1}{N_2}$
$=\frac{2A_1}{A_1}\times \frac{2N_2}{N_2}=\frac{4}{1}$