N atoms of a radioactive substance emit n `alpha`-particles per second. The half life of the radioactive substance is

Options

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

Answer

C

Explanation

Number of `alpha`-particles emitting
per second `=(dN)/(dt)`
`=lambda N`
`=n`
`:. lambda =n/N`
`:. T=0.693/lambda=(0.693 N)/n`