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
Answer & explanation
Correct answer: option 4
$N_1 = N_0 e^{-10\lambda t} , N_2 = N_0 e^{-\lambda t}$
$ \frac{N_1}{N_2} = e^{-9\lambda t} = \frac{1}{e} = e^{-1}$
$\Rightarrow 9\lambda t =1 $
$\Rightarrow t = \frac{!}{9\lambda}$