Two radioactive materials X₁ and X₂ have decay constant 5 and , respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that X₂ will be 1 / e after a time

Step-by-step solution

Decays constants of radioactive materials X₁ and X₂ is given as ₁=5 and ₂= If N₀ be the initial number of nuclei in both radioactive materials, then according to radioactive decay law, aligned & N_ X₁ &=N₀ e^ - ₁ t and & N_ X₂ &=N₀ e^ - ₂ t & & N_ X₁ N_ X₂ &= N₀ e^ - ₁ t N₀ e^ - ₂ t aligned aligned 1 e &=e^ (- ₁+ ₂ ) t [ Given , N_ X₁ N_ X₂ = 1 e ] e⁻¹ &=e^ - ( ₁- ₂ ) t ( ₁- ₂ ) t &=1 t &= 1 ₁- ₂ &= 1 5 - = 1 4 aligned