Fluorine-18 is a radioactive isotope that decays to form oxygen-18 via first-order kinetics. It takes 1.83 hr for half of a sample of F-18 to decay.

a) What is the rate constant for the decomposition of fluorine-18?

b) 18F is used to study the brain by injecting fluoro-substituted glucose into the patients bloodstream. The glucose accumulates in the brain's active regions and needs nourishment. 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 18F to decay?