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

Answer

D

Explanation

`(N_(x_(1))(t))/(N_(x_(2))(t))=1/eimplies (N_(0)e^(-10 lambdat))/(N_(0)e^(-lambdat))=1/e`
(Intially both have same number of nuclei say `N_(0)`)
`implies e=.^(-lambdat)//e^(-10 lambdat)implies e=e^(9lambdat), lambda_(1)=10 lambda` and `lambda_(2)=lambda`
`=9lambda t=1 implies t=1/(9 lambda)`