my_wits_end (my_wits_end) wrote in physics,
my_wits_end
my_wits_end
physics

Radioactive Iodine Activity

I'm trying to help someone with this physics problem and it's not going well...
A patient with thyroid problems has radioactive iodine-123 deposited in his thyroid gland. If the iodine-123 has an initial activity of 2.4 MBq, what is its activity after 18 days?

This has got to be easy but I have something going conceptually wrong. The practice version is slightly different and I know the answer so I will demonstrate with that one:
A patient with thyroid problems has radioactive iodine-123 deposited in his thyroid gland. If the iodine-123 has an initial activity of 2.7 MBq, what is its activity after 15 days?

Since the unit Becquerels is a measure of number of nuclear decays per second, I just assume that it can be used the same way that grams is used in the following equation, since grams of radioactive atoms should be directly proportional to the number of nuclear decays per second.

A = A0e-(lambda*t), where lambda = ln(2)/half-life

The half-life of I-123 is 13.13 hours, so lambda = 0.0527911....
The time t = 15 days * 24 hours/day = 360 hours
A0 = 2.7E6 Bq

Therefore, A = 2.7E6e-(0.0527911*360) = 1.5055E-2 Bq, or 15,055 microBq
The answer, however, is supposed to be 16,700 microBq.

Is my assumption incorrect? Should I be using a different formula?
Thanks for any help.
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