There are two radioactive substances A and B . Decay constant of B is two times that of A . Initially, both have an equal number of nuclei. After n half lives of A , rate of disintegration of both are equal. The value of n is

Step-by-step solution

Let λ A = λ ∴ λ B = 2 λ If N 0 is total number of atoms in A and B at t = 0 , then initial rate of disintegration of A = λ N 0 , and initial rate of disintegration of B = 2 λ N 0 As λ B = 2 λ A ∴ T B = 1 2 T A i e , half-life of B is half the half-life of A . After one half-life of A - d N d t A = λ N 0 2 Equivalently, after two half lives of B - d N d t B = 2 λ N 0 4 = λ N 0 2 Clearly, - d N d t A = - d N d t B after n = 1 i e , one half-life of A