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

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(4) 40 s. Let the two masses be equal at time t; each decays with its own half-life. A₁: 40(1/2)^t/20 and A₂: 160(1/2)^t/10. Setting them equal, (160)/(40)=(1/2)^t/20-t/10=2^t/20. 4=2^t/20, so t/(20)=2 and t=40 s. Check: in 40 s, A₁ has had 2 half-lives (40→10 g) and A₂ has had 4 (160→10 g).

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

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