• # question_answer Two radioactive materials A and B have decay constants$10\lambda$and$\lambda ,$respectively. It initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time : [JEE Main 10-4-2019 Morning] A) $\frac{11}{10\lambda }$                              B) $\frac{1}{9\lambda }$C) $\frac{1}{10\lambda }$                                D) $\frac{1}{11\lambda }$

${{N}_{1}}={{N}_{0}}{{e}^{-10\lambda t}}$           ${{N}_{2}}={{N}_{0}}{{e}^{-\lambda t}}$           $\frac{1}{e}=\frac{{{N}_{1}}}{{{N}_{2}}}={{e}^{-9\lambda t}}$ $\Rightarrow 9\lambda t=1$ $t=\frac{1}{9\lambda }$