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Two radioactive material $A_{1}$ and $A_{2}$ have decay constant of $10 λ_{0}$ and $λ_{0}$ initially they have same
number of nuclei, then after time $\frac{1}{9 λ_{0}}$ the ratio of number of their undecayed nuclei will be :

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$\frac{\sqrt{e}}{1}$

$\frac{1}{e^{2}}$

$\frac{1}{e^{3}}$

$\frac{1}{e}$

answer is A.

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Detailed Solution

$\frac{N_{1}}{N_{2}} = \frac{e^{- λ_{1} t}}{e^{- λ_{2} t}} = e$

$(λ_{0} - 10 λ_{0}) \times \frac{1}{9 λ_{0}} = \frac{1}{e}$

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