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NEET 2008 (AIPMT) · Law of Radioactive Decay

Law of Radioactive Decay question from NEET 2008 (AIPMT)

Q106NEET 2008 · AIPMTMedium

Law of Radioactive Decay

Two radioactive materials X1 and X2 have decay constants $5\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that X2 will be 1/e after a time

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Answer: (a)

$\frac{N_1}{N_2} = \frac{e^{-5\lambda t}}{e^{-\lambda t}} = e^{-4\lambda t}$ .
$e^{-4\lambda t} = e^{-1} \Rightarrow t = \frac{1}{4\lambda}$ .
So the answer is (a) $1/4\lambda$ .

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