A thyroid cancer patient is given a dosage of ^131I (half-life = 8.1 d). What fraction of the dosage of 131I will still be in the patient's thyroid after 32.4 days?
We can use the formula for radioactive decay to calculate the fraction of the dosage of ^131I remaining in the patient's thyroid after 32.4 days.
The general formula for radioactive decay is:
N(t) = N0 * (1/2)^(t/T)
Where:
N(t) = the amount of radioactive substance remaining after time t
N0 = the initial amount of radioactive substance
t = time passed
T = the half-life of the radioactive substance
Given that the half-life of ^131I is 8.1 days, we can substitute the values into the formula:
N(32.4) = N0 * (1/2)^(32.4/8.1)
N(32.4) = N0 * (1/2)^4
N(32.4) = N0 * 1/16
N(32.4) = N0 * 0.0625
Therefore, after 32.4 days, 6.25% (or 0.0625 fraction) of the dosage of ^131I will still be in the patient's thyroid.