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Two radioactive materials $X_{1} and X_{2}$ have decay constants $11 λ$ and $λ$ respectively. If initially they have same number of nuclei, then the ratio of number of nuclei of $X_{1} and X_{2}$ will be $\frac{1}{e^{2}}$ after a time

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$\frac{1}{11 λ}$

$\frac{1}{5 λ}$

$\frac{1}{9 λ}$

$\frac{1}{10 λ}$

answer is A.

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Detailed Solution

$\begin{array}{l} N_{1} = N_{0} e^{- 11 λt} \to (1) \\ N_{2} = N_{0} e^{- λt} \to (2) \end{array}$

It is given that $\frac{N_{1}}{N_{2}} = \frac{1}{e^{2}}$ , solving the about 2 equations, $t = \frac{1}{5 λ}$

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