Q86 / 120 · NEET 2012 (Mains) · Physics
The half life of a radioactive nucleus is 50 days. The time interval $\left(t_2-t_1\right)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and the time $t_1$ when $\frac{1}{3}$ of it had decayed is
- A30 days
- Correct answerB50 days
- C60 days
- D15 days
Solution
Active fraction at instant $t_2$,
$$
\frac{1}{2^{t_2 / T_{1 / 2}}}=\frac{1}{3}
$$
Active fraction at instant $t_1$,
$$
\begin{aligned}
\frac{1}{2^{t_1 / T_{1 / 2}}} & =\frac{2}{3} \\
\frac{2^{t_2 / T_{1 / 2}}}{2^{t_1 / T_{1 / 2}}} & =2 \\
t_2-t_1=T_{1 / 2} & =50 \text { days }
\end{aligned}
$$
Hence, the correct answer is option: 'B'.