Final answer:
It takes 16 days for a 100-gram sample of Iodine-131 to decay to 25 grams, because the half-life of Iodine-131 is 8 days and two half-lives would be required for this level of decay.
Step-by-step explanation:
The question involves calculating the amount of time it takes for a radioactive substance to decay to a certain amount, using its known half-life. In this case, the half-life of Iodine-131 is 8 days, and we need to determine how long it takes for a 100-gram sample to decay to 25 grams. Since 25 grams is one-fourth of the original amount, this means that two half-lives would have passed because:
- After 1 half-life (8 days), 100 g would reduce to 50 g.
- After 2 half-lives (16 days), 50 g would reduce to 25 g.
Therefore, it would take 16 days for a 100-gram sample of Iodine-131 to decay to 25 grams.