Two radioactive substances A and B have decay constants 5 λ and λ respectively. At t = 0 , a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become 1 e 2 will be

Step-by-step solution

Using the decay equation, N = N 0 e - λ t For radioactive substance A , N 1 = N 0 e - 5 λ t ...........(i) For radioactive substance B , N 2 = N 0 e - λ t ............(ii) From equation (i) and (ii) N 1 N 2 = e - 5 λ t e - λ t 1 e 2 = e - 4 λ t 4 λ t = 2 Time taken, t = 1 2 λ