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Law of Radioactive Decay question from NEET 2017

Q88NEET 2017Medium

Law of Radioactive Decay

Radioactive material 'A' has decay constant '8 $\lambda$ ' and material 'B' has decay constant ' $\lambda$ '. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be e?

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Answer: (a)

$\frac{N_B}{N_A} = \frac{e^{-\lambda t}}{e^{-8\lambda t}} = e^{7\lambda t}$ .
$e^{7\lambda t} = e \Rightarrow t = \frac{1}{7\lambda}$ .
So the answer is (a) $\frac{1}{7\lambda}$ .

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