Two radioactive materials have decay constant `5lambda&lambda`. If initially they have same no. of nuclei. Find time when ratio of nuclei become `((1)/(e))^(2)` :

Answer

D

Explanation

`N = N_(0)e^(-lambdat)`
`N_(A) = N_(0)e^(-5lambdat)`
`N_(B) = N_(0)e^(-lambdat)`
`(N_(A))/(N_(B)) = e^(-4lambdat) rArr ((1)/(e))^(2) = ((1)/(e))^(4lambdat)`
`4lambdat = 2 rArr t = (1)/(2)lambda`