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

Question

Two radioactive substances A and B have decay constants $5 λ$ and $λ$ respectively. At $t = 0$ , they have the same number of nuclei. The ratio of number of nuclei of A to that of B will be $(1 / e)^{2}$ after a time interval of

A

$\frac{1}{λ}$

B

$\frac{1}{2 λ}$

C

$\frac{1}{3 λ}$

D

$\frac{1}{4 λ}$

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Updated on : 2022-09-05

Solution

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Correct option is B)

We know that: $N = N_{0} e^{- λ t}$
For A: $N_{A} = N_{0} e^{- 5 λ t}$
For B: $N_{B} = N_{0} e^{- λ t}$

Given: $\frac{N _{A}}{N _{B}} = \frac{1}{e ^{2}}$

$\Rightarrow \frac{N _{A}}{N _{B}} = \frac{1}{e ^{4 λ t}}$

$\Rightarrow t = \frac{1}{2 λ}$

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