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. ` 4 lamda `
B. ` 2 lamda `
C. ` ( 1 ) /( 2lamda ) `
D. ` ( 1 ) /( 4lamda ) `

Answer

C

Explanation

At t=0, `N=N_(0)` for both the substances A and B
`therefore N_A=N_(0)e^(-lambda_(gl)) and N_(B)=N_(a)e^(-lambda_(gl))`
`(N_(A))/(N_(B))=(e^(-lambda_(A^(t))))/(e^(-lambda_(g t)))=e^((lambda_(H)-lambda_(A))t)=e^((lambda-5lambda)t`
`"As" (N_(A))/(N_(B))=((1)/(e))^(2)["According to question"]`
`or t=(2)/(4lambda)=(1)/(2lambda)`