A radioactive nucleus can decay by two different processes. The half lives of the first and second decay processes are `5 xx 10^(3)` and `10^(5)` years respectively, Then, the effective half-life of the nucleus is,

Options

A. `105xx10^(5) yr`
B. 4762 yr
C. `10^(4) yr`
D. 47.6 yr

Explanation

The effective half - life of the nucleus
`lambda=lambda_(1)+lambda_(2)`
`(0.69)/(T)=(0.69)/(T_(1))+(0.69)/(T_(2))`
`T=(T_(1)T_(2))/(T_(1)+T_(2))`
`=(5xx10^(3)xx10^(5))/(5xx10^(3)[1+20])=(5xx10^(5))/(105)`
=4762 yr