Patients with Graves disease have an overactive thyroid gland. A common treatmen
ID: 1484693 • 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 1014 atoms of the isotope 131I, 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 x1014 131I atoms. What is the maximum delay before the pill is no longer usable?
Explanation / Answer
here,
initial concentration of the Pills , C0 = 4 * 10^14 atoms
half life , Th = 8 days = 192 hrs
a)
when t = 24 hours
number of half lifes , n = 24/192
n = 0.125
the concentartion left , C= ( 1/2)^0.125 * C0
C =( 1/2)^0.125 * ( 4 * 10^14 )
C= 3.67 * 10^14 atoms
the atoms delivered to the hospital is 3.67 * 10^14 atoms
b)
minimum amount of atoms , C= 1.1 * 10^14 atoms
let the number of half lifes be n
C = ( 1/2)^n * C0
1.1 * 10^14 = (1/2)^n * 4 * 10^14
n = 1.86
the maximum delay = n * half life = n * 8 days = 14.88 days
the maximum delay before the pill is no longer usable is 14.88 days