Q50 / 66 · JEE Advanced 2008 (Paper 2) · Physics
A radioactive sample $S_1$ having an activity of $5 \mu \mathrm{Ci}$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10 \mu \mathrm{Ci}$. The half lives of $S_1$ and $S_2$ can be
- Correct answerA20 yr and 5 yr, respectively
- B20 yr and 10 yr, respectively
- C10 yr each
- D5 yr each
Solution
Activity of $S_1=\frac{1}{2}$ (activity of $S_2$ )
or
$$
\lambda_2 N_1=\frac{1}{2}\left(\lambda_2 N_2\right) \text { or } \frac{\lambda_1}{\lambda_2}=\frac{N_2}{2 N_1}
$$
or
$$
\begin{aligned}
& \frac{T_1}{T_2}=\frac{2 N_1}{N_2}\left(T=\text { half-life }=\frac{\ln 2}{\lambda}\right) \\
& N_1=2 N_2 \\
& \frac{T_1}{T_2}=4
\end{aligned}
$$
Given
$\therefore$ correct option is (a).
Hence, the correct answer is option: 'A'.