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MHT CET 2024 (16 May, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from MHT CET 2024 (16 May, Shift 2)

Q22MHT CET 2024 · 16 MAY · SHIFT 2Medium

Law of Radioactive Decay

Two radioactive substances A and B have decay constants ' $5\lambda$ ' and ' $\lambda$ ' respectively. At $t = 0$ , they have the same number of nuclei. The ratio of number of nuclei of $A$ to those of $B$ will be $\left(\frac{1}{e}\right)^2$ after a time interval

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Answer: (d)

$\frac{N_A}{N_B} = \frac{e^{-5\lambda t}}{e^{-\lambda t}} = e^{-4\lambda t}$ .
$e^{-4\lambda t} = e^{-2} \Rightarrow t = \frac{1}{2\lambda}$ .
So the answer is (d) $\frac{1}{2\lambda}$ .

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