Question

A patient is injected with a solution of 1.2 mg of ¹³¹I to test for thyroid uptake. The injection occurred at 3 PM Monday. The procedure to assay the thyroid is at 9 AM Thursday. ¹³¹I has a half-life of 192.5 hrs. How much of the original iodine is still in the patient at the Thursday appointment?

A. 868 ug

B. 0.47 mg

C. 90 mg

D. 0.946 mg

E. Not enough information

Answer 1

Answer - D 0.946 mg

Radioactive decay equation

Given ,the initial amount Ao= 1.2 mg and the half life of 131 I =192.5 hours

Monday 3PM to thursday 9 AM = 24+24+18 = 66 hours

First we need to calculate the decay constant of the 131I

Decay constant (K)= inverse of the mean lifetime (average life time of drug before decay)

Decay constant = ln2 /t1/2 = 0.6931/ 192.5 = 0.0036 hour

Final amount AF = unknown

AF = Ao e-kt   = 1.2 mg X2.7182 -0.0036x 66.  = 0.946174 mg

e = mathematical constant = 2.7182