Two radioactive samples X and Y initially have activities 800 Bq and 100 Bq. Their half-lives are 2 h and 6 h respectively. After how many hours will their activities become equal?
Physics · Nuclear physics · radioactivity and law of decay
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Question

Two radioactive samples X and Y initially have activities 800 Bq and 100 Bq. Their half-lives are 2 h and 6 h respectively. After how many hours will their activities become equal?

G1 Physics · Accepted Answer

Write the activity laws: A(X) = 800×2^(−t ÷ 2) A(Y) = 100×2^(−t ÷ 6). At equality: 800×2^(−t ÷ 2) = 100×2^(−t ÷ 6). Divide by 100: 8 = 2^[t ÷ 2 − t ÷ 6]. Since 8 = 2³: 3 = t(1 ÷ 2 − 1 ÷ 6) = t ÷ 3. Therefore, t = 9 h. Hence N = 9.