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
Nuclear fission product
Fission products have half-lives of 90 years (samarium-151) or less, except for seven long-lived fission products that have half lives of 211,100 years (technetium-99) and more. Therefore, the total radioactivity of a mixture of pure fission products decreases rapidly for the first several hundred years (controlled by the short-lived products) before stabilizing at a low level that changes little for hundreds of thousands of years (controlled by the seven long-lived products).