Two radioactive `X_(1)` and `X_(2)` have decay constants `10 lambda ` and `lambda` respectively . If initially they have the same number of nuclei, then the ratio of the number of nuclei of `X_(1)` to that of `X_(2)`will be `1//e` after a time .

Options

A. `1//(10 lamda)`
B. `1//(11 lamda)`
C. `11//(10 lamda)`
D. `1//(9 lamda)`

Answer

D

Explanation

(d) `N_1 = N_0 e^(-10 lamda t)` and `N_2 = N_0 e^(-lamda t)`
`rArr (N_1)/(N_2) = (1)/(e) = e^(-1) = e^((10 lamda + lamda)) = e^(9 lamda t) rArr t = (1)/(9 lamda)`.