Question

Iodine-131 is administered orally in the form of NaI(aq) as a treatment for thyroid cancer. The half-life of iodine-131 is 8.04 days. If you begin with 28.7 mg of this isotope, what mass remains after 13.4 days have passed?

Answer 1

7.175 mg

Step-by-step explanation:

The half-life of a radioactive isotope is the amount of time it takes for half of the original amount of the isotope to decay. After one half-life, the mass of the isotope will be reduced to half of its original value. After two half-lives, the mass will be reduced to a quarter of its original value, and so on.

In the case of iodine-131, the half-life is 8.04 days. After 13.4 days, two half-lives have passed because 13.4 days / 8.04 days/half-life = 1.667 half-lives. This means that the mass of iodine-131 will be reduced to a quarter of its original value, or 28.7 mg / 4 = 7.175 mg. Therefore, after 13.4 days, 7.175 mg of iodine-131 will remain.