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 = N ₀ e ^ - t N ₁= N ₀ e ^ -5 t ...(i) and N ₂= N ₀ e ^ - t ...(ii) Dividing equation (i) by equation (ii), we get, aligned & N₁ N₂ =e^ (-5 + ) t =e^ -4 t = 1 e^ 4 t & N₁ N₂ = ( 1 e )^2= 1 e^2 ...[Given] & 1 e^2 = 1 e^ 4 t & 2=4 t t= 2 4 = 1 2 aligned