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.