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 4:00 P.M. the next day? (Assume no excretion of the nuclide from the body.)

Express your answer using two significant figures.

m =

  μg  

Answer 1

Given:

Half life = 8.0 days = 8.0*24 hours = 1.92*10^2 hours

use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(1.92*10^2)

= 3.609*10^-3 hours-1

we have:

[A]o = 1.1 ug

t = 32 hours

k = 3.609*10^-3 hours-1

use integrated rate law for 1st order reaction

ln[A] = ln[A]o - k*t

ln[A] = ln(1.1) - 3.609*10^-3*32

ln[A] = 9.531*10^-2 - 3.609*10^-3*32

ln[A] = -2.019*10^-2

[A] = e^(-2.019*10^-2)

[A] = 0.980 ug

Answer: 0.980 ug