A radioactive nucleus can decay by two different processes. Half-life for the first process is 3 . 0 hours while it is 4 . 5 hours for the second process. The effective halflife of the nucleus will be

Step-by-step solution

Here the particle is decayed by two processes with decay constant λ 1 and λ 2 . Radioactive decay rate is directly proportional to number of nucleus present at any time, so total rate of decay is d A d t - - λ 1 A + - λ 2 A ⇒ d A d t = - λ 1 + λ 2 A ⇒ λ eff   = λ 1 + λ 2 ⇒ ln 2 t 1 2 eff = ln 2 t 1 2 1 + ln 2 t 1 2 2 ⇒ t 1 2 off   = 4 . 5 × 3 7 . 5 hours = 1 . 8 hours