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Two radioactive materials x₁ and x₂have decay constant $10 λ$ and $λ$ respectively. Initially they have the same number of nuclei. The ratio of the number of nuclei x₁ to that of x₂ will be $(1 / e)$ , after time :

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$\frac{1}{10 λ}$

$\frac{1}{11 λ}$

$\frac{11}{10 λ}$

$\frac{1}{9 λ}$

answer is D.

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Detailed Solution

From $N = N_{0} e^{- λ_{1} t}$
$\frac{N_{1}}{N_{2}} = \frac{e^{- λ_{1} t}}{e^{- λ_{2} t}} \Rightarrow \frac{1}{e} = e^{(λ_{2} - λ_{1}) t}$
$\frac{1}{e^{1}} = e^{- 9 λ t} = \frac{1}{e^{9 λ t}} \Rightarrow t = \frac{1}{9 λ}$

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