Radioactive decay obeys a first-order rate law, and its rate is often reported in terms of half-life, the time necessary for half the radioactive nuclei to decompose. Known half-lives of isotopes such as $${}_{\text{6}}^{\text{14}}\text{C}$$ and $${}_{\text{92}}^{\text{238}}\text{U}$$ may be used to establish the ages of objects containing these elements, provided accurate measurements can be made of the quantity of radiation emitted. Geiger-Müller counters or scintillation counters are often used for such measurements. Other important applications of radioactive isotopes include tracer studies, where a particular type of atom can be labeled and followed throughout a reaction, and neutron activation analysis, which can determine extremely low concentrations of many elements.
The relative stability of a nucleus is given by the energy of formation per nuclear particle. This may be determined from the difference between the molar mass of the nucleus and the sum of the molar masses of its constituent protons and neutrons. Both fission, breaking apart of a heavy nucleus, and fusion, combining of two light nuclei, can result in release of energy. Fission usually involves $${}_{\text{92}}^{\text{238}}\text{U}$$ or , $${}_{\text{94}}^{\text{239}}\text{Pu}$$ and these isotopes have been used in nuclear explosives and nuclear power plants. Fission products are highly radioactive. Because of the considerable damage done to living tissue by the ability of α, β and γ radiation to break bonds and form ions, emission of radioactive materials must be carefully controlled and fission power plants are quite expensive to construct. Although it promises much larger quantities of free energy and fewer harmful by-products than fission, nuclear fusion bas not yet been shown to be feasible for use in power plants. So far its only application has been in hydrogen bombs.