CHEMISTRY !! help

Question

A patient is injected with 7.08 μCi of radioactive iodine-131 with a half-life of 8.02 days. Assuming that 90.0% of the iodine ultimately finds its way to the thyroid, what decay rate (or activity) do you expect to find in the thyroid after 35 days?

Answer 1

This would be a first order decay, so we can use the expression...

fraction remaining = 0.5ⁿ where n is the number of half lives that have elapsed

fraction remaining = ?

n = number of half lives elapsed = 35 days x 1 half life/8.02 days = 4.36 half lives

fraction remaining = 0.5^4.36

fraction remaining = 0.0487

This would be the fraction of the 90% that reached the thyroid.

You started with 7.08 uCi and 90% reached the thyroid. Thus, 7.08 uCi x 0.90 = 6.37 uCi reached the thyroid

After 35 days, the activity in the thyroid would be 6.37 uCi x 0.0487 = 0.310 uCi