<P> In terms of separate decay constants, the total half - life T 1 / 2 (\ displaystyle T_ (1 / 2)) can be shown to be </P> <Dl> <Dd> T 1 / 2 = ln ⁡ 2 λ c = ln ⁡ 2 λ 1 + λ 2 . (\ displaystyle T_ (1 / 2) = (\ frac (\ ln 2) (\ lambda _ (c))) = (\ frac (\ ln 2) (\ lambda _ (1) + \ lambda _ (2))).) </Dd> </Dl> <Dd> T 1 / 2 = ln ⁡ 2 λ c = ln ⁡ 2 λ 1 + λ 2 . (\ displaystyle T_ (1 / 2) = (\ frac (\ ln 2) (\ lambda _ (c))) = (\ frac (\ ln 2) (\ lambda _ (1) + \ lambda _ (2))).) </Dd> <P> For a decay by three simultaneous exponential processes the total half - life can be computed as above: </P>

Show that radioactive decay is exponential in nature