Uranium–uranium dating
U, with a half-life of about 4.5 billion years, decays to U through emission of an alpha particle to thorium-234 (Th), which is comparatively unstable with a half-life of just 24 days. Th then decays through beta particle emission to protactinium-234 (Pa)). This decays with a half-life of 6.7 hours, again through emission of a beta particle, to U. This isotope has a half-life of about 245,000 years. The next decay product, thorium-230 (Th), has a half-life of about 75,000 years and is used in the uranium-thorium technique. Although analytically simpler, in practice U/U requires knowledge of the ratio at the time the material under study was formed and is generally used only for samples older than the ca. 450,000 year upper limit of the Th/U technique. For those materials (principally marine carbonates) for which these conditions apply, it remains a superior technique.
Nuclear binding energy
The curve of binding energy is a graph that plots the binding energy per nucleon against atomic mass. This curve has its main peak at iron and nickel and then slowly decreases again, and also a narrow isolated peak at helium, which as noted is very stable. The heaviest nuclei in nature, uranium U, are unstable, but having a half-life of 4.5 billion years, close to the age of the Earth, they are still relatively abundant; they (and other nuclei heavier than helium) have formed in stellar evolution events like supernova explosions preceding the formation of the solar system. The most common isotope of thorium, Th, also undergoes alpha particle emission, and its half-life (time over which half a number of atomformula_1s decays) is even longer, by several times. In each of these, radioactive decay produces daughter isotopes that are also unstable, starting a chain of decays that ends in some stable isotope of lead.