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

Answer

D

Explanation

`N_(x_(1)) =N_(0) e^(-10 lambda t)`
`N_(x_(2)) =N_(0) e^(-lambda t)`
`(N_(x_(1)))/(N_(x_(2)))=(1)/(e)=(e^(-10lambdat))/(e^(-lambdat))=e^(9lambda)`
`9 lambda t =1 rArr t=(1)/(9lambda)`.