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

Answer

B

Explanation

`because N = N_0e^(-lamdat)` after time 't'
`therefore N_1 = N_0 e^(-5lamdat) " and " N_2 = N_0 e^(-lamda t)`
`therefore N_1/N_2 = e^((-5 + 1)lamdat) = e^(-4lamdat)`
`N_1/N_2 " should be " 1/e therefore 1/e = e^(-4lamdat) = (1)/(e^(4lamdat))`
`therefore 4lamda t = 1 therefore t = (1)/(4lamda)`