Question

The greatest concentration of iodine in the body is in the thyroid gland, so radioactive iodine-131 is often used as a tracer to help diagnose thyroid problems. Suppose the activity of 131I in a patient’s thyroid is initially 1.85 × 106 Bq. 131I decays via beta radiation with an average energy of 180.0 keV per decay. Calculate the absorbed dose in sieverts the patient’s thyroid receives in the first hour of exposure. Assume that half of the radiation is absorbed by the thyroid gland, which has a mass of 23.0 g. The relative biological effectiveness for beta radiation is 1.00 Sv/Gy.

________Sv.

Answer 1

Activity (dN/dt) of ¹³¹I at time t is given by

where (dN/dt)_o = 1.85 10⁶ Bq , is activity at initial time and is decay constant of Iodine.

Half-life of ¹³¹I is 8.04 days . Hence decay constant is given by

Number of disintegrations for 1 hour from initial time t=0 is given by

By substituting in the above equation, we get n = 6.65 10⁹ disintegrations

If each disintegration gives an average 180 keV -ray and 50% of radiation is absorbed , then absorbed energy E by thyroid is given as

E =0.5 6.65 10⁹ 180 1.602 10^-16 J = 9.588 10^-5 J

Absorbed dose of thyroid = absorbed energy / mass of thyroid = 9.588 10^-5 J / ( 23 10^-3 ) kg

Absorbed dose of thyroid = 4.168 10^-3 Gy

Dose equivalent = 4.168 10^-3 Sv