# The half-life of I-131 is 8.00 days. If a medical treatment involves a dose of 400. mg of I-131, how much of the isotope remains after 48 days?

3.125 mg

6.25 mg

12.5 mg

25 mg

## 6.25

Thank you.

## To determine how much of the isotope remains after 48 days, we need to use the concept of half-life.

The half-life of I-131 is given as 8.00 days. This means that every 8.00 days, the amount of I-131 will be reduced by half.

To find out how many half-lives have passed after 48 days, we divide the total time (48 days) by the half-life (8.00 days):

48 days / 8.00 days/half-life = 6 half-lives

Since each half-life reduces the amount of I-131 by half, we can calculate the remaining amount by multiplying the initial dose (400. mg) by 0.5 raised to the power of the number of half-lives:

Remaining amount = Initial dose × (0.5)^(number of half-lives)

Remaining amount = 400. mg × (0.5)^6

Remaining amount ≈ 400. mg × 0.015625

Remaining amount ≈ 6.25 mg

Therefore, after 48 days, approximately 6.25 mg of I-131 remains. So the correct answer is 6.25 mg.