Question

Patients with Graves disease have an overactive thyroid gland. A common treatment uses radioactive iodine, which is taken up by the thyroid. A patient ingests a single iodine pill and it is known that the dose equivalent absorbed by the patient's 40.0 g thyroid gland is 160 rem.

In each decay of ¹³¹I, a beta particle with an energy of 620 keV is released and RBE_beta = 1. If the thyroid gland absorbs 70% of the energy of each beta particle, how many decays correspond to the known dose equivalent?

5.82 x 10¹⁰ decays

2.59 x 10¹⁰ decays

1.28 x 10¹¹ decays

9.22 x 10¹¹ decays

8.58 x 10¹¹ decays

Answer 1

The equivalent dose is 160 rem = 1.6 Sv. If the RBE factor is equal to 1 this means the absorbed dose is also 1.6 Sv. So the amount of energy absorbed by the thyroid must be

But the absorption in the gland is only 70% effective, so the energy required from the iodine is

Finally since each decay of I releases 620 keV we'll need