Carbon dating: Every living thing absorbs Carbon, including the relatively rare isotope 14C (about 1% of all Carbon isotopes). Carbon-14 is radioactive by beta-emission, with a half-life of about 5700 years. When the specimen dies, it stops absorbing Carbon, and so by measuring the amount of 14C present in a sample, and comparing that to a comparable living specimen, one can get an estimate of the sample's age.
Sterilization of equipment and food: The fact that radiation can destroy biological material is used in the sterilization of medical equipment, where a lack of contamination is essential. More controversial is the same use on food, where it is used to destroy agents which hasten spoilage.
Smoke detectors: In a smoke detector, a low-level
radioactive material is present. This radiation can ionize
particles contained in smoke, which are subsequently detected
by their charge.