Define 'half life' , 'decay constant and 'mean life'of a radioactive element and write the relation connecting them.

Explanation

(i) Half life of a radioactive sample is the time taken for half the number of nuclei to disintegrated . It is denoted by `T_(1//2)`.
(ii) Mean life of a radioactive sample is defined as the ratio of sum of life times of all the individual nuclei to the total number of nuclei present in the sample. It is denoted by `tau`.
(iii) Decay constant of a radioactive substance is denined as the reciprocal of the time during which the number of nuclei of the sample reduces to `(1)/(e) or 37%` of its initial value.
(iv) Relation connecting half life, mean life and decay constant:
Half life `T_(1//2)=(0.693)/(lambda)`
Mean life `tau=(1)/(lambda)`
Dividing (1) by (2) then we have
`(T_(1//2))/(tau)=0.693`
`therefore T_(1//2)=0.693 tau.`