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
Burnup
Unprocessed used fuel from current light-water reactors consists of 5% fission products and 95% actinides, and is dangerously radiotoxic, requiring special custody, for 300,000 years. Most of the long-term radiotoxic elements are transuranic, and therefore could be recycled as fuel. 70% of fission products are either stable or have half lives less than one year. Another six percent (I and Tc) can be transmuted to elements with extremely short half lives (I—12.36 hours—and Tc—15.46 seconds). Zr, having a very long half life, constitutes 5% of fission products, but can be alloyed with uranium and transuranics during fuel recycling, or used in cladding, where its radioactivity is irrelevant. The remaining 20% of fission products, or 1% of unprocessed fuel, for which the longest-lived isotopes are Cs and Sr, require special custody for only 300 years. Therefore, the mass of material needing special custody is 1% of the mass of unprocessed used fuel.