Question:
A radioactive sample disintegrates via two independent decay processes having half lives $\mathrm{T}_{1 / 2}^{(1)}$ and $\mathrm{T}_{1 / 2}^{(2)}$ respectively. The effective half- life $\mathrm{T}_{1 / 2}$ of the nuclei is:
Correct Option: , 3
Solution:
(3)
$\lambda_{\text {eq }}=\lambda_{1}+\lambda_{2}$
$\frac{1}{\mathrm{~T}_{1 / 2}}=\frac{1}{\mathrm{~T}_{1 / 2}^{(1)}}+\frac{1}{\mathrm{~T}_{1 / 2}^{(2)}}$
$\mathrm{T}_{1 / 2}=\frac{\mathrm{T}_{1 / 2}^{(1)} \mathrm{T}_{1 / 2}^{(2)}}{\mathrm{T}_{1 / 2}^{(1)}+\mathrm{T}_{1 / 2}^{(2)}}$
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