43-3 A Natural Nuclear Reactor

43-3 A Natural Nuclear Reactor#

Prompts

  • Today \(^{235}\text{U}\) is ~0.7% of natural uranium. Why was it ~3% about 2 billion years ago? Use the half-lives of \(^{235}\text{U}\) (704 My) and \(^{238}\text{U}\) (4.5 Gy) to explain.

  • What geological conditions at Oklo (Gabon) allowed a natural chain reaction? Think about enrichment, moderator, and geometry (sections 43-1, 43-2).

  • How was the Oklo reactor self-regulating? What happened when the reaction heated the water?

  • Evidence for the natural reactor: anomalous isotope ratios of fission products. Why would fission products have different ratios than naturally occurring elements?

  • Could a natural reactor form today? Why or why not?

Lecture Notes#

Overview#

  • The Oklo uranium deposit in Gabon is the only known site where a natural nuclear chain reaction occurred — about 2 billion years ago.

  • At that time, \(^{235}\text{U}\) was ~3% of uranium (vs ~0.7% today) because it decays faster than \(^{238}\text{U}\). Combined with the right geology (ore concentration, water as moderator), a critical chain reaction was possible.

  • Evidence includes depleted \(^{235}\text{U}\) and anomalous isotope ratios of fission products that cannot be explained by normal geological processes.

Why 2 Billion Years Ago?#

Natural uranium today is ~99.3% \(^{238}\text{U}\) and ~0.7% \(^{235}\text{U}\). The half-life of \(^{235}\text{U}\) is 704 My; \(^{238}\text{U}\) is 4.5 Gy. Because \(^{235}\text{U}\) decays faster, its fraction decreases over time.

About 2 billion years ago, \(^{235}\text{U}\) was ~3% of uranium — high enough that, with sufficient ore concentration and a moderator, a chain reaction could be sustained. Earlier, the ratio was even higher, but the right geological conditions may not have existed.

Exponential decay

From \(N = N_0 e^{-\lambda t}\) (section 42-3), the ratio \(N_{235}/N_{238}\) decreases as we move forward in time (since \(\lambda_{235} > \lambda_{238}\)). Going back in time, the ratio was higher: \(R_{\text{past}} = R_{\text{today}}\,e^{(\lambda_{235}-\lambda_{238})t}\) for \(t\) years ago.

Geological Conditions at Oklo#

For a natural chain reaction (sections 43-1, 43-2), the following were needed:

  1. Enrichment: ~3% \(^{235}\text{U}\) (provided by the ancient isotopic ratio).

  2. Concentration: Uranium ore rich enough to approach critical mass.

  3. Moderator: Groundwater (water) slowed neutrons to thermal energies where the fission cross section is large.

  4. Geometry: Ore bodies of sufficient size to retain neutrons.

Self-Regulation#

The Oklo reactor was self-regulating. When the chain reaction ran, it heated the water. Water boiled away → less moderator → fewer thermal neutrons → reaction slowed or stopped. When the water cooled and returned, moderation resumed → reaction could start again. This cyclic behavior prevented a runaway; the reactor operated intermittently over hundreds of thousands of years.

Evidence#

The Oklo deposit was discovered in 1972 when routine analysis showed depleted \(^{235}\text{U}\) — some ore had less \(^{235}\text{U}\) than the natural ratio. The only explanation: fission had consumed it.

Additional evidence: anomalous isotope ratios of fission products (e.g., Nd, Ru). These elements have fission-product isotopes with ratios that differ from those found in natural, non-irradiated uranium. The pattern matches the expected yields from \(^{235}\text{U}\) fission.

Summary#

  • Oklo: natural fission chain reaction ~2 billion years ago.

  • \(^{235}\text{U}\) was ~3% then (vs 0.7% today) due to its shorter half-life.

  • Conditions: ore concentration, water as moderator, suitable geometry.

  • Self-regulation: water boiled away when hot → reaction stopped; water returned → reaction could resume.

  • Evidence: depleted \(^{235}\text{U}\), anomalous fission-product isotope ratios.