Iodine-125 (125I) is used to treat, among other things, brain tumors and prostat

Question

Iodine-125 (125I) is used to treat, among other things, brain tumors and prostate cancer. It decays by gamma decay with a half-life of 54.90 days. Patients who fly soon after receiving 125I implants are given medical statements from the hospital verifying such treatment because their radiation could set off radiation detectors at airports.

If the initial decay rate (or activity) was 532 Ci, what will the rate be after 365.0 days?

How many months after the treatment will the decay rate be reduced to 15.5% of the original value? Assume months of 30 days.

Explanation / Answer

first, let's calculate the constant k:

k = ln2/t1/2
k = ln2/54.9 = 0.01263 days-1

To calculate the concentration:

C = Co exp(-kt)
C = 532 exp(-0.01263*365)
C = 5.2946 uCi

If the dacay it's reduced to it's 15.5% of it's original value:

0.155Co = Co exp(-'0.01263*t)
0.155 = exp(-0.01263*t)
ln(0.155) = -0.01263t
t = ln(0.155)/-0.01263
t = 147.61 days ----> 147.61 days * 1 month/30 days = 4.92 months or simly 5 months.

Hope this helps

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