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 interval

Step-by-step solution

Number of nuclei remained after time t can be written as N=N₀ e^ - t where N₀ is initial number of nuclei of both the substances. and aligned & N₁=N₀ e^ -5 t (i) & N₂=N₀ e^ - t (ii) aligned Dividing Eq. (i) by Eq. (ii), we obtain N₁ N₂ =e^ (-5 + ) t =e^ -4 t = 1 e^ 4 t But, we have given N₁ N₂ = ( 1 e )^2= 1 e^2 Hence, 1 e^2 = 1 e^ 4 t Comparing the powers, we get or aligned & 2=4 t & t= 2 4 = 1 2 aligned