Final answer:
After 24 days, which equals three half-lives of Iodine-131 (8 days per half-life), the activity of a 32 mCi sample reduces to 4 mCi due to radioactive decay.
Step-by-step explanation:
Iodine-131 has a half-life of 8.0 days. Given that the initial activity of an I-131 sample is 32 mCi, we want to calculate its activity after 24 days. To do this, we need to determine how many half-lives have passed in 24 days and then apply the concept of radioactive decay.
Since each half-life is 8 days, 24 days is equal to three half-lives (24 / 8 = 3). After each half-life, the activity of the sample is halved. Therefore, after three half-lives:
- After the first half-life (8 days), the activity is halved from 32 mCi to 16 mCi.
- After the second half-life (16 days), the activity is again halved from 16 mCi to 8 mCi.
- After the third half-life (24 days), the activity is halved once more from 8 mCi to 4 mCi.
Thus, the activity of the I-131 sample after 24 days is 4 mCi.