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)` :

Options

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

Answer

C

Explanation

At `t=0, N=N_(0)` for both the substances A and B
`N_(1)=N_(e) e^(-lambda_(1)t)` and `N_(2)=N_(0) e^(-lambda_(2)t)`
`(N_(1))/(N_(2))= e^(-lambda_(1)t)/(e^(-lambda_(1)t)) =e^((lambda_(2)-lambda_(1)t))= e^((lambda-5lambda)t)`
`e(-4lambdat)=(1/e)^(4lambdat)`
`(N_(1))/(N_(2))=(1/e)^(2) :. 4lambdat=2 or t= 2/(4lambda)=1/(2lambda)`