At time t = 0 , a material is composed of two radioactive atoms A and B , where N A ( 0 ) = 2 N B ( 0 ) The decay constant of both kind of radioactive atoms is λ . However, A disintegrates to B and B disintegrates to C . Which of the following figures represents the evolution of N B t N B 0 with respect to time t ?

Step-by-step solution

The rate at which nuclei of B is forming, d N B d t = λ N A - λ N B d N B d t = 2 λ N B 0 e - λ t - λ N B e - λ t d N B d t + λ N B = 2 λ N B 0 e - λ t e λ t d d t N B e - λ t = 2 λ N B 0 on integrating above the equation, N B e λ t = 2 λ t N B + N B 0 N B e λ t = 2 λ t N B 0 + N B 0 N B = N B 1 + 2 λ t e - λ t d d t N B = 0 - λ 1 + 2 λ t e - λ t + 2 λ e - λ t = 0 N B m a x a t t = 1 2 λ