Chapter 12, Problem 46E

Fluorine-18 is a radioactive isotope that decays by positron emission to form oxygen-18 with a half-life of 109.7 min. (A positron is a particle with the mass of an electron and a single unit of positive charge; the equation is $\text{F}\to \text{O}+\text{e}$ Physicians use ${}^{\text{18}}\text{F}$ to study the brain by injecting a quantity of ?uoro-substituted glucose into the blood of a patient. The glucose accumulates in the regions where the brain is active and needs nourishment.

(a) What is the rate constant for [lie decomposition of ?uorine-18?

(b) If a sample of glucose containing radioactive fluorine-18 is injected into the blood, what percent of the radioactivity will remain after 5.59 h?

(c) How long does it take for 99.99% of the ${}^{\text{18}}\text{F}$ to decay?