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 the initial number of nuclei of both materials be N₀ . The number of nuclei of material A at time t is given by N_A = N₀ e^ -7 t . The number of nuclei of material B at time t is given by N_B = N₀ e^ - t . Given that the ratio of the number of nuclei of material B to that of A is e : N_B N_A = e N₀ e^ - t N₀ e^ -7 t = e e^ 6 t = e^1 Equating the powers of e , we get: 6 t = 1 t = 1 6 Answer: 1/6