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 days

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

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(8)

= 8.662*10^-2 days-1

we have:

[A]o = 1.1 ug

t = 24 hours + 8 hours

= 1 day + 1/3 days

= 1.33 days

k = 8.662*10^-2 days-1

use integrated rate law for 1st order reaction

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

ln[A] = ln(1.1) - 8.662*10^-2*1.33

ln[A] = 9.531*10^-2 - 8.662*10^-2*1.33

ln[A] = -1.99*10^-2

[A] = e^(-1.99*10^-2)

[A] = 0.980 ug

Answer: 0.980 ug