Suppose a patient is given 140mg of I−131, a beta emitter with a half-life of 8.0 days.
Assuming that none of the I−131 is eliminated from the person's body in the first 4.0 hours of treatment, what is the exposure (in Ci) during those first four hours?
Express your answer using two significant figures.
To determine the exposure (in Ci) during the first four hours of treatment, we need to calculate the amount of I-131 that remains in the person's body after four hours.
Given:
Initial amount of I-131 = 140 mg
Half-life of I-131 = 8.0 days
First, we need to convert the half-life to hours since we are interested in the exposure during the first four hours. There are 24 hours in a day, so:
Half-life of I-131 = 8.0 days x 24 hours/day = 192 hours
We can use the radioactive decay formula to calculate the remaining amount of I-131 after four hours:
Amount remaining = Initial amount x (1/2)^(time/half-life)
Plugging in the values:
Amount remaining = 140 mg x (1/2)^(4 hours / 192 hours)
Calculating (1/2)^(4/192):
(1/2)^(4/192) ≈ 0.9723
Amount remaining = 140 mg x 0.9723
Calculating 140 mg x 0.9723:
Amount remaining ≈ 136.22 mg
Now, we can convert the remaining amount from milligrams (mg) to curies (Ci). To do this, we need to know the specific activity of I-131 in curies per milligram (Ci/mg).
Let's assume the specific activity of I-131 is 1.0 Ci/mg.
Exposure (in Ci) during the first four hours = Amount remaining (in mg) x Specific activity (in Ci/mg)
Plugging in the values:
Exposure = 136.22 mg x 1.0 Ci/mg
Calculating 136.22 mg x 1.0 Ci/mg:
Exposure ≈ 136.22 Ci
Therefore, the exposure (in Ci) during the first four hours is approximately 136.22 Ci.