Prozac (fluoxetine hydrochloride) is a selective serotonin reuptake inhibitor (SSRI) used to treat depression. Its function in the brain can be studied by using radiolabeled ¹⁸F instead of natural abundance fluorine in its structure. The positron emission is detected by a PET scan. 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?

Question

Quizplus · Accepted Answer

To find when the activity reaches 10% of the original, we need to calculate how many half-lives it takes for the substance to decay to 10% of its initial amount. The formula for decay is $A = A_0 \times (1/2)^{t/T}$, where $A$ is the final activity, $A_0$ is the initial activity, $t$ is the time elapsed, and $T$ is the half-life. To reach 10%, or $A/A_0 = 0.1$, we solve $0.1 = (1/2)^{t/109.7}$. Solving for $t$ gives approximately 3 half-lives (since $(1/2)^3 = 0.125$ is close to 0.1). Three half-lives of 109.7 minutes each total approximately 329.1 minutes, or about 5.5 hours. Adding 5.5 hours to 8:00 A.M. gives approximately 1:30 P.M., with the closest answer being 2:04 P.M., Monday.

Prozac (Fluoxetine Hydrochloride) Is a Selective Serotonin Reuptake Inhibitor (SSRI)