Patients with Graves disease have an overactive thyroid gland. A common treatmen
ID: 1477845 • Letter: P
Question
Patients with Graves disease have an overactive thyroid gland. A common treatment uses radioactive iodine, which is taken up by the thyroid. The radiation emitted in its decay will destroy the tissues of the gland. A single pill is produced with 4 x 10^14 atoms of the isotope 131 I, which has a half life time of 8 days. a)How many atoms remain 24 hrs after the pill’s creation, when the pill is delivered to the hospital? b) Although the iodine in the pill Is constantly decaying, it is still usable as long as it contains at least 1.1 x10^14 (131) I atoms. What is the maximum delay before the pill is no longer usable?
Explanation / Answer
a) Decay constant, = (ln 2) / t1/2 = (ln 2) / (8 * 24) = 0.0036 per hour
Atoms remaining after 24 hours, A = (4 * 1014) e-(0.0036 * 24) = 3.67 * 1014 atoms
b) Let 't' be the maximum delay.
Then,
1.1 * 1014 = (4 * 1014)e-0.0036t
=> t = (1 / 0.0036) * ln[(4 * 1014) / (1.1 * 1014)] = 358.6 hours = 14.94 days