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Activity is given by A = −dN/dt = −λN. Activity at time t₁ is A₁ = −λN₁ and activity at time t₂ is A₂ = −λN₂. As t₁ > t₂, therefore, number of atoms remained after time t₁ is less than that remained after time t₂. That is, N₁ < N₂. ∴ number of nuclei decayed in (t₁ − t₂) is N₂ − N₁ = (A₁ − A₂)/λ.

1. A₁ − A₂
2. (A₁ − A₂)/λ
3. λ(A₁ − A₂)
4. λ(A₂ − A₁)

Correct answer: (A₁ − A₂)/λ

Solution

The number of nuclei decayed in the time interval (t₁ − t₂) is given by the difference in the number of nuclei at t₂ and t₁, which is N₂ − N₁. Using the relation A = λN, we can express this as (A₁ − A₂)/λ. Hence, the correct answer is (B).

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