Question

The biological activity of some organs can be investigated using radioactive isotopes. For example, iodine is important in the action of the thyroid. A subject is injected with a small amount of radioactive 131 I and after a few days, the following measurements are made with a Geiger counter:

1.) The counter is placed in contact with the abdomen and 2750 counts/s are observed six days later, the counter records 600 counts/s?

2.) With the counter over the thyroid, 5,500 counts/s are observed and six days later 3290 counts/s are observed?

a) If the physical half life of 131 I is 194 hr, what is the biological half life of iodine in the bulk of the human body?

b) What can you say about iodine in the thyroid?

The answer is supossed to be 100 hrs.

Answer 1

For every half life, the activity of the radio isotope will become half of the previous activity.

For 131 Iodine, the half life is 194 hrs which is 8 days 2 hours.

In six days, counts at the abdomen has become 600 and 3290 in thyroid..

Lets say 600+3290 = (5500+2750)* (1/2)^n where n half lives have already passed. Solving gives n = 1.08 half lives

6 days = 6*24 = 144 hrs = 1.08 half lives

1 half life = 144/1.08 = 133 hrs.

The Iodine in thyroid decayed lot slower than the iodine in the rest of the body and the activity is high. This shows that the patient has extreme amounts of iodine and he is suffering wth the symptoms of thyroid.