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The half life of a radioactive nucleus is 50 days. The time interval (t₂ - t₁) between the time when 2/3 of it has decayed and the time t₁ when 1/3 of it had decayed is:

1. 30 days
2. 50 days
3. 60 days
4. 15 days

Correct answer: 60 days

Solution

The fraction of undecayed nuclei is given by N/N₀ = (1/2)^(t/T). For 1/3 decayed, N/N₀ = 2/3, and for 2/3 decayed, N/N₀ = 1/3. Solving for t₁ and t₂ using the half-life T = 50 days, we find t₁ = 50 log(3/2)/log(2) and t₂ = 50 log(3)/log(2). The difference t₂ - t₁ simplifies to 50 days.

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