Radioactivity is the conversion of one nuclear state to another. It is accompanied by the emission of particles or electromagnetic radiation. The nuclear state change can often involve a change in the atomic number of the atoms involved. The most well known forms of radiation emiited are alpha particles (helium nuclei - two protons bound with two neutrons), beta particles (energetic electrons) and gamma radiation (very high energy electromagnetic radiation). Another form of radioactivity is fission in which a nucleus splits into two smaller components.
Natural Sources of Radiation
Most sources of natural, predictable radiation come from the decay of atomic nuclei, resulting in either alpha - or beta - particles. In general, decay is more common among the heavier elements, as it reduces the proton:neutron ratio, while decay is much more prominent among lighter elements, as it converts a neutron into a proton.
Two prominent examples of radioactive decay are:
This is the first decay in the famous Uranium decay. U-238 is essentially non-radioactive (especially compared to hyper-active U-235), and has a half-life of over four billion years.
This is the decay that allows for carbon dating, and has a half-life of over 5000 years.
Gamma radiation is much more difficult to come by, as emitting a gamma ray does not allow an atomic nuclei to decay. The most famous source of high-energy gamma rays is what happens when an electron and a positron annihilate:
Since positrons are relatively rare, this is an interaction that is relatively hard to find. However there are fairly reliable sources of radiation, including Cesium-137 and Cobalt-60. Both are useful for a wide variety of technical purposes, as well as for their utility in cancer treatment.