Two radioactive substances A and B have decay constants 5 and respectively. At t=0 , they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1 / e^2 ) after a time

Step-by-step solution

At t=0, N=N₀ for both the substances A and B aligned & N_A=N₀ e^ - _A t and N_B=N_o e^ - _ B^t & N_A N_B = e^ - _A t e^ - _B t =e^ ( _B- _A ) t =e^ ( -5 ) t & =e^ -4 t = ( 1 e )^ 4 t aligned As N_A N_B = ( 1 e )^2 [According to question] 4 t=2 or t= 2 4 = 1 2