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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 $5 λ a n d λ$ respectively. Initially both A and B have the same number of nuclei. The ratio of the number of nuclei of A to that of B will be $\frac{1}{e}$ after a time

A

$\frac{1}{5 λ}$

B

$\frac{1}{4 λ}$

C

$\frac{5}{4 λ}$

D

$\frac{4}{5 λ}$

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Updated on : 2022-09-05

Solution

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Correct option is B)

Using the law of radioactivity, we can write:
$\frac{N ( 5 λ )}{N ( λ )} = \frac{N _{0} e ^{- 5 λ t}}{e ^{- λ t}}$

$\frac{1}{e} = \frac{e ^{- 5 λ t}}{e ^{- λ t}}$

$e^{- 1} = e^{- 4 λ t}$

$- 1 = - 4 λ t \Rightarrow t = \frac{1}{4 λ}$

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