What is the half-life of I-131 if it decays 10 microcuries to 5 microcuries in 10 days?

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justaguide eNotes educator| Certified Educator

The the rate of decay of the element I-131 decreases from 10 microcuries to 5 microcuries in 10 days. Curie is the non-SI unit of radioactivity and is equal to 3.7*10^10 decays per second.

Half life of an element undergoing decay is the time taken for the initial amount of a substance to decrease to half the value. As the amount of a substance decreases so does the rate of decays per second. In the case of I-131 after 10 days the number of decays after ten days has reduced to half the number of decays taking place initially.

Else, use the relation N(t) = N0*(1/2)^(t/th) where th is the half life.

5 = 10*(1/2)^(10/th)

=> 1/2 = (1/2)^(10/th)

=> 10/th = 1

=> th = 1

The half life of I-131 is 10 days.