Two radioactive materials `X_1` and `X_2` have decay constants `10 lamda` and `lamda` 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 lambda`
B. `1 // 11 lambda`
C. `11//10 lambda`
D. `1//9 lambda`

Answer

D

Explanation

`N_(1) = N_(0) e^(-10 lambda t) , N_(2) = N_(0) e^(- lambda t)`
`(N_(1))/(N_(2)) = e^(-9 lambda t) = e^(-1) , 9 lambda t = 1 implies t = (1)/(9 lambda)`