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.
MOX fuel
Plutonium-241 is fissile while the isotopes of plutonium with even mass numbers are not (in general thermal neutrons will usually fission isotopes with an odd number of neutrons, but rarely those with an even number), so decay of plutonium-241 to americium-241 leaves plutonium with a lower proportion of isotopes usable as fuel, and a higher proportion of isotopes that simply capture neutrons (though they may become fissile isotopes after one or more captures). The decay of plutonium-238 to uranium-234, and subsequent removal of this uranium, would have the opposite effect, but plutonium-238 both has a longer half-life (87.7 years vs. 14.3) and is a smaller proportion of the spent nuclear fuel. Plutonium-239, -240, and -242 all have much longer half-lives so that decay is negligible. Plutonium-244 has an even longer half-life, but is unlikely to be formed by successive neutron capture because plutonium-243 quickly decays with a half-life of 5 hours giving americium-243.