Two radioactive materials `X_1` and `X_2` have decay constants `10 lambda` and `lambda`, respectively. If initialy 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
(a) `1//10 lambda` (b) `1//11 lambda` (c) `11//10lambda` (d) `1//9lambda`

Options

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

Answer

D

Explanation

`N_(1)=N_(0)e^(-10 lamda t)` and `N_(2)=N_(0)e^(-lamdat)`
`rArr (N_(1))/(N_(2))=(1)/(e)=e^(-1)=e^((-10 lamda+lamda)t)=e^(-9 lamda t) rArr t = (1)/(9 lamda)`.