Correct option : (2)
Explanation:
Denoting by λ1 and λ2 the decay constants of the two modes by which nucleus can decay we have
The probability that an active nucleus decay by first mode in a small time dt is λ1 dt and that for the second mode is λ2 dt. Then the probability that it decays either by first process or second process is (λ1 dt + λ2 dt).
Now we can say that λ is the effective decay constant. Hence the probability that the nucleus decay by effective value of λ in small time dt is λdt.
Hence we must have