A radioactive sample decays by -emission. In first two seconds ‘n… - Vidyadip

MCQ

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 ...... $sec$

A
$2$
B
$4$
✓
$1$
D
None of these

✓

Answer

Correct option: C.

$1$

c
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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