During mean life of a radioactive element, the fraction that disintegrates is

Options

A. e
B. `(1)/( e)`
C. `(e - 1)/( e)`
D. `( e)/( e - 1)`

Answer

C

Explanation

(c ) By using `N = N_0 e^(-lamda t)` and average life time `t = (1)/(lamda)`
So `N = N_0 e^(-lamda xx 1//lamda) = N_0 e^-1 rArr (N)/(N_0) = e^-1 = (1)/(e )`
Now disintegrated fraction
=`1 - (N)/(N_0) = 1- (1)/( e) = (e - 1)/( e)`.