N atoms of a radioactive element emit n number of `alpha`-particles per second. Mean life of the element in seconds, is

Options

A. `(n)/(N)s`
B. `(N)/(n)s`
C. `(0.693N)/(n)s`
D. `(0.693n)/(N) s`

Answer

C

Explanation

`(dN)/(dt)= - lamda N rArr n= - lamda N [" as " (dN)/(dt)= n]`
`therefore lamda = (-n)/(N)`
Half life `= (l n 2)/(|lamda|)= (0.693)/(n) sec`