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

Answer

A

Explanation

`x_(1)=N_(0)e^(-5lambdat)`
`x_(2)=N_(0)e^(-lambdar)`
`(x_(1))/(x_(2))=e^(-5lambdat+lambdat)`
`(1)/(e)=e^(-4lambdat)`
`e^(-1)=e^(-4lambdat) rArr t=(1)/(4lambda)`