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 calculate the exposure (in Ci) during the first four hours, we need to consider the decay of I-131 over time.

First, let's convert the initial amount of I-131 given to the patient (140 mg) into units of Ci. To do this, we need to know the specific activity of I-131, which is the activity per unit mass.

The specific activity of I-131 can be found by dividing the activity (in Ci) by the mass (in grams) of the sample. Let's assume the specific activity of I-131 is 10 Ci/g. Therefore, the activity of 140 mg of I-131 is:

Activity = Specific Activity × Mass
= 10 Ci/g × (140 mg ÷ 1000 g/mg)
= 1.4 Ci

Now, let's calculate the amount of I-131 remaining after 4.0 hours. Since the half-life of I-131 is 8.0 days, we can use the radioactive decay formula:

Amount remaining = Initial amount × (1/2)^(time/half-life)

Substituting the values:

Amount remaining = 1.4 Ci × (1/2)^(4 h / (8 days × 24 h/day))
= 1.4 Ci × (1/2)^(4/192)
≈ 1.4 Ci × 0.976

Approximately, the amount of I-131 remaining after 4.0 hours is 1.363 Ci (rounded to three decimal places).

Finally, to calculate the exposure during those four hours, we assume that all the remaining I-131 contributes to the exposure. Hence, the exposure after 4.0 hours is approximately 1.363 Ci.

Therefore, the exposure (in Ci) during the first four hours is 1.4 Ci (rounded to two significant figures).