Two radioactive materials A and B having decay constant '7 ' and ' ' respectively, initially have same number of nuclei. The time taken to have the ratio of number of nuclei of material B to that of A as ' e ' is

Step-by-step solution

Let N_A(t) and N_B(t) denote the number of nuclei of materials A and B at time t , with initial quantity N₀ for both. The decay follows N(t) = N₀ e^ - t , where the decay constants are _A = 7 and _B = . Thus, N_A(t) = N₀ e^ -7 t and N_B(t) = N₀ e^ - t . Given the ratio condition: N_B(t) N_A(t) = e Substituting the expressions yields: N₀ e^ - t N₀ e^ -7 t = e^ 6 t = e Equating exponents gives 6 t = 1 , so t = 1 6 , corresponding to option B. Final Answer: B