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Two radioactive materials A and B contain same number of nuclei. If $8 {λs}^{- 1}$ and $3 {λs}^{- 1}$ are the decay constants of A and B respectively. The ratio of number of nuclei undecayed of A to that of B will be $(\frac{1}{e})$ after a time.

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$\frac{1}{2 λ} s$

$\frac{1}{8 λ} s$

$\frac{1}{5 λ} s$

$\frac{1}{11 λ} s$

answer is C.

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Detailed Solution

$N = N_{0} e^{- λt}$

$\frac{N_{A}}{N_{B}} = \frac{N_{0} e^{- 8 λt}}{N_{0} e^{- 3 λt}} \Rightarrow \frac{1}{e} = e^{- 5 λt}$

$t = \frac{1}{5 λ}$

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