Radioactive isotopes are useful as they can be detected. Detecting these waves can help us find problems within the body and come up with prognoses. An example of this is PET scans. These use substances that undergo beta-plus decay (positron emission) such as radioactive glucose as a tracer to go around the body and help us detect abnormalities in the body.
These medical practices tend to use beta decay or gamma emission due to their good penetration but lower ionisation, reasons alpha decay is not useful. We need good penetration so that the emission is able to leave the body, but also low ionisation so the patient is at less risk due to radiation. Half lives are also important factors for radioactive detection, as a half life is needed so that the patient is not exposed for too long, nor are they isolated for too long, nor leave the hospital still emitting radiation. One also needs a half life that is long enough to travel around the body. For this reason, a half life of a few hours is ideal.