Two radioactive materials `X_1` and `X_2` have decay constants `10 lamda` and `lamda` respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of `X_1` to that of `X_2` will be `1//e` after a time.

Options

A. `(1)/(10lamda)`
B. `(1)/(11lamda)`
C. `(11)/(10lamda)`
D. `(1)/(9lamda)`

Answer

A

Explanation

`N=N_0e^(-lamdat) therefore (N_(X_1))/(N_(X_2)) = (N_0e^(-10lamdat))/(N'_0e^(-lamdat))`
initially both of them have the same bumber of nuclei,
i.e. `N_0 = N'_0`
`therefore (N_(X_1))/(N_(X_2)) = e^(-9lamdat)`
But it is given that ` (N_(X_1))/(N_(X_2)) = 1/e = e^(-1)`
`therefore 9 lamda t = 1 " or " t = (1)/(9lamda)`