Two radioactive materials A and B have decay constants 25 λ and 16 λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be " e " after a time 1 a λ . The value of a is _____ .

Step-by-step solution

According to radioactive decay formula, N = N 0 e - λ t , here, N 0 is the initial number of nuclei in a radioactive material. Given here, λ 1 = 25 λ and λ 2 = 16 λ . And N B N A = e For radioactive material A , N A = N 0 e - λ 1 t For radioactive material B , N B = N 0 e - λ 2 t Thus, the ratio N B N A = e - λ 2 t e - λ 1 t = e - λ 2 t · e λ 1 t ⇒ e 1 = e λ 1 - λ 2 t ⇒ λ 1 - λ 2 t = 1 Time, t = 1 λ 1 - λ 2 = 1 25