A radioactive sample S₁ having the activity A ₁ has twice the number of nuclei as another sample S₂ of activity A₂ . If A₂=2 A₁ , then the ratio of half-life of S₁ to the half-life of S₂ is

Step-by-step solution

Activity, A = N = 0.693 ~T _ 1 / 2 ~N where T _ 1 / 2 is the half-life of a radioactive sample. aligned A ₁ ~A ₂ &= N ₁ ~T ₁ T ₂ ~N ₂ T ₁ ~T ₂ &= A ₂ ~A ₁ N ₁ ~N ₂ &= 2 ~A ₁ ~A ₁ 2 ~N ₂ ~N ₂ = 4 1 aligned