A radioactive nucleus decays by two different processes. The half-life for the first process is 10 s and that for the second is 100 s . The effective half-life of the nucleus is close to:

Step-by-step solution

Using the equation of radioactive decay law, - d N d t = λ 1 N + λ 2 N     . . . ( 1 ) - d N d t = λ 1 + λ 2 N     . . . ( 2 ) Where, - d N d t is the rate of decay λ 1 ,   λ 2 are decay constant for two different processes N is the number of atoms. Now applying the decay law for the combine process, we get - d N d t = λ e f f N     . . . ( 3 ) Equating equation (1) and (2) we get λ e f f = λ 1 + λ 2     . . . ( 4 ) Now t