Radioactive decay is the natural process whereby certain chemical elements with an unstable nucleus transform into other chemical elements by emitting either an alpha-particle (two neutrons and two protons) or a beta-particle (an electron) along with a gamma ray photon.
At the level of a single atom, radioactive decay is unpredictable. However, for a group of atoms, the probability of how many will undergo radioactive decay is very predictable. A "half-life" is the period of time where 50% of atoms in a given sample of an identical atom will undergo radioactive decay. This period can be as short as a fraction of a second or for some elements, like uranium, can be hundreds of millions of years. The danger of a particular atom to human health from radiation is related to the length of its half-life.
Radioactive decay was discovered accidentally when a sample of pitchblend, a by-product of silver mining, was placed next to a photographic plate and exposed the film even though the plate was kept away from light. Although radioactive decay was at first though to be related to X-rays, it was soon clear that the phenomena was much more complicated.
Radioactive decay is used in medicine for several purposes, including the use of radioactive atoms of cobalt as part of radiation therapy, and the use of other radioactive atoms in tracers used in a PET scan.