Two radioactive materials X₁ and X₂ have decay constants $10\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of number of nuclei of X₁ to that of X₂ will be 1/e after time

$\frac{1}{9\lambda}$

$N_1 = N_0 e^{-10\lambda t} , N_2 = N_0 e^{-\lambda t}$

$ \frac{N_1}{N_2} = e^{-9\lambda t} = \frac{1}{e} = e^{-1}$

$\Rightarrow 9\lambda t =1 $

$\Rightarrow t = \frac{!}{9\lambda}$