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JEE Main 2021 (18 Mar, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2021 (18 Mar, Shift 1)

Q55JEE Main 2021 · 18 MAR · SHIFT 1Easy

Law of Radioactive Decay

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 T1/2 of the nuclei is:

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Answer: (c)

Both processes act together, so $\lambda = \lambda_1 + \lambda_2$ .
With $\lambda = \frac{\ln2}{T}$ : $\frac{1}{T_{1/2}} = \frac{1}{T_{1/2}^{(1)}} + \frac{1}{T_{1/2}^{(2)}}$ .
$T_{1/2} = \frac{T_{1/2}^{(1)}T_{1/2}^{(2)}}{T_{1/2}^{(1)}+T_{1/2}^{(2)}}$ , so the answer is (c).

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