Fluorine-18, which is often used in PET scans to locate tumors, decays to form a positron and oxygen-18.After 90.0 minutes, 1.00 18O is present relative to every 1.30 18F.Estimate the half-life of F-18.

Question

Quizplus · Accepted Answer

The decay of Fluorine-18 (F-18) can be analyzed using the formula for radioactive decay, $N = N_0 \times (1/2)^{t/T}$, where $N$ is the remaining quantity of the substance, $N_0$ is the initial quantity, $t$ is the time elapsed, and $T$ is the half-life of the substance. Given that after 90 minutes, the ratio of $^{18}O$ to $^{18}F$ is 1.00 to 1.30, it means that for every 2.30 parts of the mixture, 1.30 parts are $^{18}F$, implying that $^{18}F$ has decayed to 1.30/2.30 of its original amount. Solving the decay formula for $T$ with $t = 90$ minutes and $N/N_0 = 1.30/2.30$, we find that the half-life of F-18 is approximately 109 minutes.

Fluorine-18, Which Is Often Used in PET Scans to Locate