A source contains two independent radioactive isotopes X and Y. Initially each isotope contributes an activity of 1600 Bq. The half-life of X is 2 h and the half-life of Y is 4 h. If the total activity after 4 h is N Bq, find N.
Physics · Nuclear physics · radioactivity and law of decay
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Question

A source contains two independent radioactive isotopes X and Y. Initially each isotope contributes an activity of 1600 Bq. The half-life of X is 2 h and the half-life of Y is 4 h. If the total activity after 4 h is N Bq, find N.

Physics · Nuclear physics · radioactivity and law of decay

G1 Physics · Accepted Answer

For isotope X, 4 h corresponds to two half-lives: A(X) = 1600 ÷ 2² = 400 Bq. For isotope Y, 4 h corresponds to one half-life: A(Y) = 1600 ÷ 2 = 800 Bq. Total activity: A(total) = 400+800 = 1200 Bq. Hence N = 1200.