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