​ A radioactive sample disintegrates via two independent decay processes having half lives T(1/2)^(1)and T(1/2)^(2) respectively.

Question

A radioactive sample disintegrates via two independent decay processes having half lives \(T^{(1)}_{1/2}\) and \(T^{(2)}_{1/2}\) respectively. The effective half-life T_1/2 of the nuclei is :

(1) None of the above

(2) T_1/2 = \(T^{(1)}_{1/2}+T^{(2)}_{1/2}\)

(3) T_1/2 = \(\frac{T^{(1)}_{1/2}T^{(2)}_{1/2}}{T^{(1)}_{1/2}+T^{(2)}_{1/2}}\)

(4)  T_1/2 = \(\frac{T^{(1)}_{1/2}+T^{(2)}_{1/2}}{T^{(1)}_{1/2}-T^{(2)}_{1/2}}\)

Answer 1

Correct option is  (3) T_1/2 = \(\frac{T^{(1)}_{1/2}T^{(2)}_{1/2}}{T^{(1)}_{1/2}+T^{(2)}_{1/2}}\)