JEE Main 2019 — Physics solution

JEE Main2019Physics

Two radioactive substances A and B have decay constants 5 $λ$ and $λ$ 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 $(\frac{1}{6})^{2}$ will be :

A
$\frac{1}{2 λ}$
B
$\frac{1}{4 λ}$
C
$\frac{1}{λ}$
D
$\frac{2}{λ}$

Solution

$N_{x} (a t t) = N_{0} e^{- 5 λ t} N_{y} (a t t) = N_{0} e^{- λ t} \frac{N _{x}}{N _{y}} = \frac{1}{e ^{2}} = e^{- 4 λ t} \Rightarrow 4 λ t = 2 \Rightarrow t = \frac{2}{4 λ} = (\frac{1}{2 λ})$

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