A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30 s . The effective half-life of the nucleus is calculated to be α 11 s . The value of α is ______.

Step-by-step solution

Decay law for both process can be written as, d N 1 d t = - λ 1 N       . . . E q ( 1 ) and d N 2 d t = - λ 2 N       . . . E q ( 2 ) Hence, net decay will become d N d t = d N 1 d t + d N 2 d t = - ( λ 1 + λ 2 ) N ⇒ λ eq = λ 1 + λ 2 ⇒ ln 2 t 1 2 = ln 2 300 + ln 2 30 ⇒ t 1 2 = 300 11 Hence, required value of α = 300 .