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>>First Order Radioactive Decay
>> $Two radioactive materials A and B have d$

Question

Two radioactive materials $A$ and $B$ have decay constants $10 λ$ and $λ$ , respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $1 / e$ after a time:

A

$\frac{1 1}{1 0 λ}$

B

$\frac{1}{9 λ}$

C

$\frac{1}{1 0 λ}$

D

$\frac{1 1}{1 1 λ}$

Medium

JEE Mains

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Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is B)

$N_{1} = N_{0} e^{- 10 λ t}$
$N_{2} = N_{0} e^{- λ t}$
$\frac{1}{e} = \frac{N _{1}}{N _{2}} = e^{- 9 λ t}$
$\Rightarrow 9 λ t = 1$
$t = \frac{1}{9 λ}$

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