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
Radium
All isotopes of radium have half-lives much shorter than the age of the Earth, so that any primordial radium would have decayed long ago. Radium nevertheless still occurs in the environment, as the isotopes Ra, Ra, Ra, and Ra are part of the decay chains of natural thorium and uranium isotopes; since thorium and uranium have very long half-lives, these daughters are continually being regenerated by their decay. Of these four isotopes, the longest-lived is Ra (half-life 1600 years), a decay product of natural uranium. Because of its relative longevity, Ra is the most common isotope of the element, making up about one part per trillion of the Earth's crust; essentially all natural radium is Ra. Thus, radium is found in tiny quantities in the uranium ore uraninite and various other uranium minerals, and in even tinier quantities in thorium minerals. One ton of pitchblende typically yields about one seventh of a gram of radium. One kilogram of the Earth's crust contains about 900 picograms of radium, and one liter of sea water contains about 89 femtograms of radium.