Question
A radioactive sample decays by $\beta$ -emission. In first two seconds $‘n’$ $\beta$ -particles are emitted and in next $2\ seconds$ , $‘0.25n’$ $\beta$ -particles are emitted. The half life of radioactive nuclei is ...... $sec$
✓
Answer
Given $\frac{N_{0}\left(1-2^{-2 / \mathrm{t}_{1 / 2}}\right)}{N_{0}\left(1-2^{-4 / \mathrm{t}_{1 / 2}}\right)}=\frac{n}{(0.25+1) n}$
{No. of $\beta$ -particles emitted $=$ No. of nuclei decayed } $\Rightarrow t_{1 / 2}=1$ $sec$
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