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The half-life of 18F is 109.7 minutes. If radiolabeled Prozac were administered to a patient for a PET scan at 8:00 A.M....

The half-life of 18F is 109.7 minutes. If radiolabeled Prozac were administered to a patient for a PET scan at 8:00 A.M.on Monday, at what time would its activity reach 10% of the original activity?

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Answer #1

Given:

Half life = 1.097*10^2 min

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

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(1.097*10^2)

= 6.317*10^-3 min-1

we have:

[A]o = 100

[A] = 10

k = 6.317*10^-3 min-1

use integrated rate law for 1st order reaction

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

ln(10) = ln(1*10^2) - 6.317*10^-3*t

2.303 = 4.605 - 6.317*10^-3*t

6.317*10^-3*t = 2.303

t = 3.645*10^2 min

= (3.645*10^2)/60 H

= 6 hours and 5 minutes

New time 8.00 AM + 6 hours and 5 minutes = 2.05 PM

Answer: 2.05 PM

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