Ionizing radiation, which is what actually causes the mutagenic changes, include the alpha/beta particles (subatomic fragments) and gamma rays (high-energy/high-frequency/short-wavelength electromagnetic radiation). Radioisotopes are the sources of the ionizing radiation--atoms with a very large nucleus that is prone to breaking up. When the nucleus of a radioisotope breaks up, energy in the form of gamma radiation and subatomic particles from the nucleus are liberated. The alpha particles (helium nuclei--two protons and two neutrons) and beta particles (high-speed electrons) can be stopped by thick clothing and similar barriers; in any event, they do not penetrate far into the skin but large amounts bombarding the skin can burn it. Gamma radiation can pass through the body just like X-rays.

A mass of a radioisotope does not decay away at a constant rate. Ionizing radiation from decay events will trigger other atoms of the radioisotope to decay. As the mass diminishes, there will be fewer decays events triggered per unit time. So, for every half-life increment of time, half of the mass at the start of the increment will decay away, and it will take many half-lives to reduce the original mass down to something close to zero.

Since there is always a low-level background radiation field from natural radioisotopes in the Earth's crust, everyone will experience some sort of chronic exposure. All this does is produce some chance that a mutagenic change due to the radiation exposure will be missed by the body's immune system and go on to form a cancerous growth. The chance of this happening seem to get better as we get older, because older bodies are not as good at chasing down and destroying mutated cells as younger ones.