A radioactive nucleus can decay by two different processes. The half-life for the first process is `t_1` and that for the second process is `t_2`. Show that the effective half-life `t` of the nucleus is given by
`1/t = 1/t_1 + 1/t_2`.

Options

A. `T=T_(1)+T_(2)`
B. `(1)/(T)=(1)/(T_(1))+(1)/(T_(2))`
C. `T=(T_(1)+T_(2))/(T_(1)T_(2))`
D. `T=(T_(1)-T_(2))/(T_(1)T_(2))`

Answer

B

Explanation

`(dN)/(dt) proplambdaN, lambda prop (1)/(T)`