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Two radioactive materials $x_{1} and x_{2}$ contain same number of nuclei. If $6 λ s^{- 1}$ and $4 λ s^{- 1}$ are the decay constants of $x_{1} & x_{2}$ respectively. The ratio of number of nuclei undecayed of $x_{1}$ to that of $x_{2}$ will be $\frac{1}{e}$ after a time

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$\frac{1}{2 λ} s$

$\frac{1}{10 λ} s$

$\frac{1}{24 λ} s$

$\frac{1}{5 λ} s$

answer is A.

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Detailed Solution

$N = N_{0} e^{- λ t} \Rightarrow \frac{N x_{1}}{N x_{_{2}}} = e^{(- 6 λ + 4 λ) t} = e^{- 1}$

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