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A mixture consists of two radioactive materials A₁ and A₂ with half lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A₁ and 160 g of A₂. The amount of the two in the mixture will become equal after:

1. 60 s
2. 80 s
3. 20 s
4. 40 s

Correct answer: 40 s

Solution

The decay of radioactive materials follows the formula N = N₀(1/2)^(t/T), where T is the half-life. For A₁ and A₂ to have equal amounts, solve 40(1/2)^(t/20) = 160(1/2)^(t/10). Simplifying gives t = 40 s.

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