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.
Uranium-238
The mean lifetime of U is 1.41 seconds divided by 0.693 (or multiplied by 1.443), i.e. ca. 2 seconds, so 1 mole of U emits 3 alpha particles per second, producing the same number of thorium-234 (Th-234) atoms. In a closed system an equilibrium would be reached, with all amounts except for lead-206 and U in fixed ratios, in slowly decreasing amounts. The amount of Pb-206 will increase accordingly while that of U decreases; all steps in the decay chain have this same rate of 3 decayed particles per second per mole U.