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

Answer

C

Explanation

`N_(1) = N_(o)e^(-10 lambda t), N_(2) = N_(o)e^(-lambdat) :. (N_(1))/(N_(2)) = (1)/(e^(9 lambdat))`
`:. (1)/(e ) = (1)/(e^(9 lambda t)) :. T = (1)/(9 lambda)`