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

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Since, we know, activity, A = λ N = 0.693 t 1 2 N ⇒ t 1 2 = 0.693 A N Thus, ( t 1 2 ) 1 ( t 1 2 ) 2 = N 1 A 1 ⋅ A 2 N 2 Given, A 2 = 2 A 1 and N 1 = 2 N 2 = 2 A 1 A 1 × 2 N 2 N 2 = 4 : 1

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