Nuclear reactor physics
Modern deposits of uranium contain only up to ~0.7% U (and ~99.3% U), which is not enough to sustain a chain reaction moderated by ordinary water. But U has a much shorter half-life (700 million years) than U (4.5 billion years), so in the distant past the percentage of U was much higher. About two billion years ago, a water-saturated uranium deposit (in what is now the Oklo mine in Gabon, West Africa) underwent a naturally occurring chain reaction that was moderated by groundwater and, presumably, controlled by the negative void coefficient as the water boiled from the heat of the reaction. Uranium from the Oklo mine is about 50% depleted compared to other locations: it is only about 0.3% to 0.7% U; and the ore contains traces of stable daughters of long-decayed fission products.Fermi age theory
Uranium-238
Thorium-234 has a mean lifetime of 3 seconds, so there is equilibrium if one mole of U contains 9 atoms of thorium-234, which is 1.5 mole (the ratio of the two half-lives). Similarly, in an equilibrium in a closed system the amount of each decay product, except the end product lead, is proportional to its half-life.