Question

At 8:00 A.M., a patient receives a 1.1-μg dose of I-131 to treat thyroid cancer. Part A If the nuclide has a half-life of 8.0 days, what mass of the nuclide remains in the patient at 8:00 P.M. the next day? (Assume no excretion of the nuclide from the body.)

Answer 1

ans)

Elapsed time = 36 hours=next day 8.00 pm

Half life = 8 days = 8 x 24 hours = 192 hours

Convert the half life to an elimination constant (k):

k = 0.693 / t_½

k = 0.693 / 192 hr

k = 0.0036 hr^-1

Formula: Cp = Cp⁰ e^-kt

where Cp = plasma concentration at time t,

Cp⁰ = initial plasma concentration = 1.1 μg,

k = elimination constant = 0.0036 hr^-1and

t = time = 36 hr.

Cp = 1.1 μg x e^(-0.0036 hr^-1 x 36 hr)                               [the hr cancel]

Cp = 1.1 μg x e^(-0.1296)                               

Cp = 1.1 μg x 0.878

Cp = 0.9658 μg approximately=0.97 μg