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.
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?
1 answer
1 answer