A radioactive sample disintegrates via two independent decay proc… - Vidyadip

MCQ

A radioactive sample disintegrates via two independent decay processes having half lives $T _{1 / 2}^{(1)}$ and $T _{1 / 2}^{(2)}$ respectively. The effective half- life $T _{1 / 2}$ of the nuclei is

A
None of the above
B
$T _{1 / 2}= T _{1 / 2}^{(1)}+ T _{1 / 2}^{(2)}$
✓
$T _{1 / 2}=\frac{ T _{1 / 2}^{(1)} T _{1 / 2}^{(2)}}{ T _{1 / 2}^{(1)}+ T _{1 / 2}^{(2)}}$
D
$T _{1 / 2}=\frac{ T _{1 / 2}^{(1)}+ T _{1 / 2}^{(2)}}{ T _{1 / 2}^{(1)}- T _{1 / 2}^{(2)}}$

✓

Answer

Correct option: C.

$T _{1 / 2}=\frac{ T _{1 / 2}^{(1)} T _{1 / 2}^{(2)}}{ T _{1 / 2}^{(1)}+ T _{1 / 2}^{(2)}}$

c
$\lambda_{ eq }=\lambda_{1}+\lambda_{2}$

$\frac{1}{ T _{1 / 2}}=\frac{1}{ T _{1 / 2}^{(1)}}+\frac{1}{ T _{1 / 2}^{(2)}}$

$T _{1 / 2}=\frac{ T _{1 / 2}^{(1)} T _{1 / 2}^{(2)}}{ T _{1 / 2}^{(1)}+ T _{1 / 2}^{(2)}}$

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