Two radioactive materials `X_(1)` and `X_(2)` have decay constant `11 lambda` and `lambda` respectively. If initially they have same number of nuclei, then ratio of number of nuclei of `X_(1)` to `X_(2)` will be `(1)/(e^(2))` after a time

Options

A. `(1)/(5 lambda)`
B. `(1)/(11 lambda)`
C. `(1)/(10 lambda)`
D. `(1)/(9 lambda)`

Answer

A

Explanation

`N_(1)=N_(o)e^(-11 lambda t)` and `N_(2) = N_(0) e^(-lambdat)` It is given that `(N_(1))/(N_(2))=(1)/(e^(2))`, solving the above two equations, we get `t=(1)/(5 lambda)`