Final answer:
Radioisotopes useful for medical diagnostics are those with a short half-life and high uptake in specific body parts, allowing for precise imaging while minimizing radiation exposure to patients.
Step-by-step explanation:
The characteristics of a radioisotope that make it useful for diagnosing medical problems are that it has a short half-life and is taken up by a specific part of the body. A short half-life ensures that the radioisotope decays quickly, minimizing the patient's exposure to radiation. The uptake by specific body parts allows for targeted imaging, where these radioisotopes can replace a stable element in a compound, now called a radiopharmaceutical, to visualize or diagnose conditions within particular organs or tissues. For example, radioactive iodine is used to monitor thyroid activity, and Technetium-99m, with a half-life of about six hours, is employed for cardiac and other organ imaging due to its ability to be taken up in areas of interest like heart muscle or inflamed regions, thus providing crucial diagnostic information.