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Two radioactive material A and B have disintegration constants 10 $λ$ and 2 $λ$ respectively. If initially they have the same number of nuclei, then the ratio of number of nuclei of A and B will be $\frac{1}{e}$ after a time of :

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$\frac{1}{8 λ}$

$\frac{11}{10 λ}$

$\frac{1}{10 λ}$

$\frac{1}{11 λ}$

answer is D.

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Detailed Solution

$\frac{[A]_{t}}{[B]_{t}} = \frac{1}{e} = \frac{e^{- 10 λ t}}{e^{- 2 λ t}}$

$\Rightarrow 1 = 8 λ t$

$\Rightarrow t = \frac{1}{8 λ}$

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