Uranium
In nature, uranium is found as uranium-238 (99.2739–99.2752%), uranium-235 (0.7198–0.7202%), and a very small amount of uranium-234 (0.0050–0.0059%). Uranium decays slowly by emitting an alpha particle. The half-life of uranium-238 is about 4.47 billion years and that of uranium-235 is 704 million years, making them useful in dating the age of the Earth.
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.