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 μCi, what will the rate be after 389.0 days?How many months will it take for the decay rate to be 16.5% of it's initial value?   Not sure how to set this problem up. Giving me a lot of trouble.

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Half life is the amount of time after which only 50% of the original quantity remains. For example, the half life of Iodine-125 is 54.9 days. This means that after 54.9 days, half of the original implant value would have decayed. Similarly, after 2 half lives or 109.8 days (=...

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Half life is the amount of time after which only 50% of the original quantity remains. For example, the half life of Iodine-125 is 54.9 days. This means that after 54.9 days, half of the original implant value would have decayed. Similarly, after 2 half lives or 109.8 days (= 2 x 54.9 days), only 25% of the original content would be left. 

The initial decay rate or activity (A0) = 532 `mu`Ci, time period = 389 days.

Decay constant, `lambda`  = 0.693/T, where T = half life = 54.9 days

Using `A = A_0 e^(-lambdat)`

Solving for a time duration, t = 389 days, we get A = 3.92 `mu`Ci

For 16.5% of the initial value, A = 16.5% of A0 = 0.165 A0

Substituting this into the equation, we get

`A/A_0 = e^(-lambdat) = 0.165`

substituting the value of decay constant, we get, t = 142.74 days.

Assuming there are 30 days in a month, it will take about 4.76 months for the activity to be 16.5% of the initial value.

Hope this helps.

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