Two radioactive materials `A_(1) and A_(2)` have decay constant `5lambda` and `lambda` respectively. If initially they have the same numberof nuclei, then ratio of nuclei of `A_(1) to A_(2)` will be `(1)/(e)` after a time :

Options

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

Answer

A

Explanation

`N_(A) = N_(0)e^(-lambda_(1)t) = N_(0)e^(-5lambdat), N_(B) = N_(0)e^(-lambda_(2)t) = N_(0)e^(-lambdat)`
`therefore (N_(A))/(N_(B)) = e^(-4lambdat ) = e^(-1) ("Given" (N_(A))/(N_(B)) = (1)/(e)) therefore 4lambdat = 1, " " t = (1)/(4lambda)`