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

(A) 1/10λ

(B) 1/11λ

(C) 11/10λ

(D) 1/9λ

Ans: (D)

Sol: $\large \frac{N_1}{N_2} = \frac{1}{e}$

$\large \frac{N_0 e^{-10\lambda t}}{N_0 e^{-\lambda t}} = \frac{1}{e}$

$\large e^{9\lambda t} = e $

$\large 9 \lambda t = 1 $

$\large t = \frac{1}{9 \lambda }$