Final answer:
After 32 days, which corresponds to four half-lives, a 1000 mg sample of iodine-131 would decay to 62.5 mg.
Step-by-step explanation:
We are dealing with the concept of half-life, which is a key topic in nuclear chemistry. To find out how much of a 1000 milligram sample of iodine-131 is left after 32 days, we consider that the half-life of iodine-131 is 8 days.
After one half-life (8 days), half of the iodine-131 would remain, so from 1000 mg we would have 500 mg.
After the second half-life (16 days), we would have half of that amount, so 250 mg remains.
Following this pattern, after the third and fourth half-lives (24 days and 32 days, respectively), we would have 125 mg and then 62.5 mg remaining.