Two radioactive substances A and B have decay constants 5λ and λ respectively. At t = 0 , a sample

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13.Nuclei

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Two radioactive substances $A$ and $B$ have decay constants $5\lambda $ and $\lambda $ respectively. At $t = 0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $(\frac {1}{e})^2$ will be

A

$1/\lambda $

B

$1/4\lambda $

C

$2/\lambda $

D

$1/2\lambda $

(JEE MAIN-2019)

Solution

$\frac{1}{{{e^2}}} = {e^{\lambda t – 5\lambda t}}$

$t\, = \,\frac{1}{{2\lambda }}$

Standard 12

Physics

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