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

Answer

A

Explanation

`X_(1) = N _(0) e ^(- lamda _(1) t ), X _(2) = N _(0) e ^(- lamda_(2)t)`
`(X _(1))/( X _(2))=e ^(-1) =e ("" ^(-lamda ) 1 + "" ^(lamda ) 2 ) ^(t),e ^(-1) =e ("" ^(-lamda ) 1 ^(-lamda ) 2)t`
`therefore t = (1)/( lamda _(1) - lamda _(2)) = (1)/((5 lamda - lamda ))= (1)/(4 lamda )`