In a radioactive disintegration, the ratio of initial number oif atoms to the number of atoms present at an instant of tme equal to its mean life is

Options

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

Answer

C

Explanation

Let the initial number of atoms at time t=0 be `N_(0)`.
Let the number of atoms at any instant of time t be N.
According to radioactive decay law `N=N_(0)e^(-lamda t)`
Mean life `tau=1//lamda`, where `lamda` is the decay constant.
here `t=tau` (given)
`:.N=N_(0)e^(-1/(tau)xxtau)` or `N=N_(0)e^(-1)` or `(N_(0))/N=e`