A radioactive sample S₁ having activity A₁ has twice the number of nuclei as another sample of S₂ of activity A₂. If A₂ = 2A₁ then the ratio of half life of S₁ to the half life of S₂ is (a) 4 (b) 2 (c) 0.25 (d) 0.75

Answer: (a). Activity A = λ N. S₁: A₁ = λ₁ (2N); S₂: A₂ = λ₂ N. A₂ = 2A₁ ⇒ λ₂ N = 4λ₁ N ⇒ λ₂ = 4λ₁. T ∝ 1/λ, so T₁/T₂ = λ₂/λ₁ = 4. So the answer is (a) 4.

A radioactive sample S₁ having activity A₁ has twice the number of… | MHT CET 2026 (15 May, Shift 1)

Q9MHT CET 2026 · 15 MAY · SHIFT 1Medium

Law of Radioactive Decay

A radioactive sample $S_1$ having activity $A_1$ has twice the number of nuclei as another sample of $S_2$ of activity $A_2$ . If $A_2 = 2A_1$ then the ratio of half life of $S_1$ to the half life of $S_2$ is

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Answer: (a)

Activity $A = \lambda N$ . $S_1$ : $A_1 = \lambda_1 (2N)$ ; $S_2$ : $A_2 = \lambda_2 N$ .
$A_2 = 2A_1 \Rightarrow \lambda_2 N = 4\lambda_1 N \Rightarrow \lambda_2 = 4\lambda_1$ .
$T \propto 1/\lambda$ , so $T_1/T_2 = \lambda_2/\lambda_1 = 4$ .
So the answer is (a) $4$ .

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