Two radioactive substance `A` and `B` have decay constants `5 lambda` and `lambda` respectively. At `t=0` they have the same number of nuclei. The ratio of number of nuclei of nuclei of `A` to those of `B` will be `(1/e)^(2)` after a time interval

Options

A. `(1)/(e)`
B. `(e)/(2)`
C. `(1)/(e^(4))`
D. `(1)/(e^(2))`

Answer

D

Explanation

`(N_(1))/(N_(2))= (N_(0) e^(- lamda_(1) t))/(N_(0) e^(- lamda_(2) t))`
`rArr (N_(1))/(N_(2))= e^(-(15x- 3x)x (1)/(6x)) rArr (N_(1))/(N_(2)) = (1)/(e^(2))`