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Initially P → 4N₀, Q → N₀. Halflife Tₚ = 1 min, T₀ = 2 min. Let after time t number of nuclei of P and Q are equal, that is 4N₀ 2^(t/1) = N₀ 2^(t/2).

1. t = 2 min
2. t = 4 min
3. t = 6 min
4. t = 8 min

Correct answer: t = 4 min

Solution

The decay equation for P is 4N₀ * (1/2)^(t/1), and for Q is N₀ * (1/2)^(t/2). Setting them equal gives 4 * (1/2)^t = (1/2)^(t/2). Simplifying, we get 4 = (1/2)^(t/2), which implies t/2 = -2 (log base 1/2 of 4). Solving, t = 4 minutes.

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