Two radioactive materials `X_(1)` and `X_(2)` have decay constants `5 lambda` and `lambda` respectively. If initially they have the same number of nuclei, then the ratio of the number of muclei of `X_(1)` to that of `X_(2)` will be `1/e` after a time

Options

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

Answer

B

Explanation

Given: `X_(1)/X_(2) =1/e` after t=?
Let initial amount = `X_(0)` at t = 0 for both nuclei. Let us assume time t be the time in which the given condition occurs.
`X_(1)/X_(2)=(X_(0)e^(-5lambdat))/X_(0)e^(-lambdat)`
`1/e=e^(-4lambdat)`
`e^(-1)=e^(-lambdat)`
`t=1/(4lambda)`