Q155 / 180 · KCET 2013 · Physics
A radioactive substance emits 100 beta particles in the first $2 \mathrm{~s}$ and 50 beta particles in the next $2 \mathrm{~s}$. The mean life of the sample is
- A$4 \mathrm{~s}$
- B$2 \mathrm{~s}$
- Correct answerC$\frac{2}{0.693} \mathrm{~s}$
- D$2 \times 0.693 \mathrm{~s}$
Solution
Given, In 1st two seconds $100 \beta$ particles and in next two seconds $50 \beta$ particles are emitted
$\begin{array}{ll}
\therefore & T_{1 / 2}=2 \mathrm{~s} \\
\text { Hence, } & T_{m}=\frac{T_{1 / 2}}{0.693}=\frac{2}{0.693}
\end{array}$
Hence, the correct answer is option: 'C'.