Two radioactive materials ' M₁ ^ and ' M₂ ^ have decay constants ' 9 ' and ' ' respectively. Initially they have the same number of nuclei. The ratio of the number of nuclei of M₁ to that of M₂ will be ' ( 1 e )^ after a time interval

Step-by-step solution

Given initial nuclei count N₀ for both materials, their quantities follow exponential decay: N₁(t) = N₀ e^ -9 t for M₁ and N₂(t) = N₀ e^ - t for M₂ , where t is time. The condition N₁(t) N₂(t) = 1 e leads to e^ -9 t e^ - t = e⁻¹ , simplifying to e^ -8 t = e⁻¹ . Equating exponents gives -8 t = -1 , so t = 1 8 . The ratio becomes 1 e at time t = 1 8 , corresponding to option D .