Final answer:
The longest half-life among PET radiotracers is F-18 at about 110 minutes; however, for diagnostic purposes, thallium-201 has an even longer half-life of 73 hours.
Step-by-step explanation:
Among the PET radiotracers listed, the one with the longest half-life is F-18, which has a half-life of approximately 110 minutes. In contrast, isotopes used in medical diagnosis, like Tc-99m, typically have much shorter half-lives to minimize radiation exposure to the patient. Tc-99m, for instance, has a half-life of about 6 hours, after which it decays to Tc-99 and emits low-intensity gamma radiation.
The radioisotope with the longest half-life is thallium-201, with a half-life of 73 hours, compared to the other commonly used medical isotopes. Such isotopes with longer half-lives provide a larger time window for conducting diagnostic procedures but can also result in increased radiation dose to the patient, necessitating careful consideration in their use.