Radiation seed therapy is a common method for treating some prostate cancers and brain tumors. Cesium-131, with a half-life of 9.7 days, is a new isotope proposed for this treatment. How long does it take for the activity of cesium-131 to decrease to 1.0% of its initial value and essentially cease to be effective?

Question

Quizplus · Accepted Answer

To solve the problem, we can use the radioactive decay formula:

Activity = Initial activity x (1/2)^(time/half-life)

We want to know the time it takes for the activity to decrease to 1.0% of its initial value, so we can set up the following equation:

0.01 x Initial activity = Initial activity x (1/2)^(time/half-life)

Simplifying, we get:

(1/2)^(time/half-life) = 0.01

Taking the natural logarithm of both sides, we get:

ln[(1/2)^(time/half-life)] = ln(0.01)

Using the property of logarithms that says ln(a^b) = b x ln(a), we can simplify the left-hand side as:

(time/half-life) x ln(1/2) = ln(0.01)

Solving for time, we get:

time = [ln(0.01)] / [ln(1/2) x (half-life)]

Plugging in the values for cesium-131 (half-life = 9.7 days), we get:

time = [ln(0.01)] / [ln(1/2) x 9.7 days] ≈ 2.1 months

Therefore, the answer is C) 2.1 mo, which is the time it takes for the activity of cesium-131 to decrease to 1.0% of its initial value and essentially cease to be effective.

Radiation Seed Therapy Is a Common Method for Treating Some