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

Let λA=λ∴λB=2λ  In N0  is total no. of atoms in A and B at t=0 ,then initial rate of disintegration of A=λN0  and initial rate of disintegration of B=2λN0 As λB=2λa    ∴TB=12TA  i.e. half life of B is half the  halflife of A. after one half life of A (−dNdt)A=λN02 Equivalently, after two half lives of B (−dNdt)B=2λN04=λN02 Clearly, (−dNdt)A=(−dNdt)B ,After n=1i.e.  one half life of A.