What were ^235U/^238U and ^238U/^232Th ratios at the start of the solar system (
ID: 108100 • Letter: W
Question
What were ^235U/^238U and ^238U/^232Th ratios at the start of the solar system (4.567 Ga ago). The ratios are 1/137.88 and 0.266 respectively. Reactor rods in nuclear power plants have Tilde 2% ^235 U. When could a uranium mine last go critical? In another words, find the time in Earth history when a uranium mine could become a natural reactor? If ^235U and ^238U are produced in the r-process with the production ratio P_235/P_238 = 1.5, find the most recent time before the solar system formed when both these nuclei could have been produced.Explanation / Answer
(a) Uranium is the most common fuel used in commercial nuclear power plants. Uranium has three isotopes: uranium-238, uranium-235, and uranium-234. Because of nuclear properties, uranium-235 is most likely to fission when bombarded with neutrons. However, on Earth today uranium-235 comprises only 0.720% of uranium while uranium-238 is the dominant isotope of uranium (99.275%) and uranium-234 is present only in trace amounts (0.006%). The isotopic distribution of uranium is remarkably uniform in Earth’s crust, so all uranium ore mined today contains about 0.720% uranium-235. In order to increase the efficiency of the nuclear chain reactions, uranium-235 is artificially enriched to approximately 3% before uranium is used as a fuel in nuclear power plants. There are four conditions which must be met in order for a stable natural nuclear reactor to develop:
- The natural uranium ore must have a high uranium content and must have a thickness (at least ~2/3 of a meter) and geometry that increase the probability of spontaneous, natural fission in uranium-238 inducing a self-sustaining fission reaction in uranium-235.
- The uranium must contain significant amount of fissionable uranium-235.
- There must be a moderator, something that can slow down the neutrons produced when uranium fissions.
- There must not be significant amounts of neutron-absorbing elements (such as silver or boron), which would inhibit a self-sustaining nuclear reaction, in the vicinity of the uranium.
The conditions necessary for a natural nuclear reactor to develop could have been present in ancient uranium deposits. Today, there are many concentrated uranium deposits, but as it is impossible for nuclear fission to spontaneously develop. This is because the concentration of uranium-235 is too small (only 0.720% of uranium, as I mentioned above) for a self-sustaining fission reaction to be sustained. However, the relative proportions of uranium-238 and uranium-235 have been changing over the history of the Earth. When the Earth was first formed, uranium-235 comprised more than 30% of uranium. The proportion of uranium-235 relative to uranium-238 has been changing because isotopes of uranium are radioactive and decay to other elements over time. However, uranium-238 decays at a much slower rate than uranium-235, so uranium-235 has become more and more depleted (relative to uranium-238) over the Earth’s 4.54 billion year history. Billions of years ago, the abundance of uranium-235 in uranium ore was high enough for a self-sustaining fission reaction to develop. Two billion years ago, there would have been about 3.6% uranium-235 present in uranium ore— about the proportion of uranium-235 used in pressurized boiling water reactor nuclear power plants.
So, in theory, an ancient (billions of years old) uranium deposit could have spontaneously developed a self-sustaining nuclear fission, assuming the uranium was concentrated enough, there was a substance (probably water) to act as a moderator, and there were not significant amounts of neutron-absorbing elements nearby. Sixteen years later, in 1972, just such a natural nuclear reactor was discovered in Gabon. The French had been mining uranium in Gabon their former colony for use in nuclear power plants. During a routine isotopic measurement of uranium ore from Gabon, the French noticed something very strange: the uranium ore did not have a uranium-235 content of 0.720%. Rather, the uranium ore was anomalously depleted in uranium-235, containing only 0.717%. This may sound like a tiny variation, but this discrepancy was very alarming for the French nuclear officials. You see, uranium-235 in Earth’s crust (and even in moon rocks and in meteorites) varies very little from the average value of 0.720%. Since uranium-235 can be used to make nuclear bombs, it was very important to account for this “missing” uranium-235. The uranium ore was depleted in uranium-235 because two billion years ago some of that uranium-235 had been used up in a natural nuclear reactor.
(b)
The initial abundances of Th and U can be derived from r-process nucleosynthesis calculations. However, the astrophysical condition of r-process is still in debate up to now. It is found that the r-process elemental abundance patterns observed from very metal-poor stars and the solar system are universal for the heavier elements above Ba. This universality suggests that there is probably only one r-process site in the Galaxy , whereas a different process could be responsible for the scatter of the lighter r-process elemental (38 6 Z 6 47, here Z is atomic number) abundance pattern. In r-process chronometers have been made so far in literatures. These works employed the solar r-process abundances to predict the zero-decay abundances of the radioactive elements.
Nevertheless, a basic hypothesis of these works is that the universal r-process abundance pattern from metal-poor stars and the solar system not only hold for the elemental abundance distribution (56 6 Z < 82) but also for the isotopic abundance distribution (A & 120). However, with improved observations of metal-poor stars (e.g., [20–23]), now it is possible to make a step further for r-process chronometers by directly simulating the abundances of very metal-poor stars thus having a more solid ground. Furthermore, by comparing the abundance patterns determined by simulating the abundances of elements in the region 38 6 Z 6 82 with those determined by simulating the abundances of elements in the region 56 6 Z 6 82, it may help to understand the uncertainty of astrophysical site(s) of r-process nucleosynthesis.
The abundances for each r-process component are calculated within the waiting-point approximation. In this method, the abundance distribution in an isotopic chain is given by the Saha equation and is entirely determined by neutron separation energies for a given temperature T, and a neutron density nn. The matter flow between neighboring isotopic chains is determined by the total -decay rates (including up to three neutrons -delay emissions). After neutron sources freeze out, all the isotopes then proceed to the corresponding stable isotopes via - and -decays. The process of spontaneous fission is also taken into account to calculate the final abundances of actinides.
During the early phase of the r-process, the waiting-point approximation is generally believed to be well maintained since the reaction rates for neutron captures and photo-dissociations are much faster than the -decay rates. Recent dynamical calculations showed that the neutron captures may influence the final abundance distribution where the corresponding neutron capture rates varied by 2 orders of magnitude. However, the Th/U ratio should not be affected dramatically in comparison to the Th/X ratio by the waiting-point approximation. Other effects induced by neutrino spallation during the freeze out may have small influence on the Th and U chronometer. Therefore, we will focus hereafter on the influence of the nuclear ground state properties within the waiting-point approximation. The astrophysical condition of r-process nucleo-sythesis can be obtained by the best fit to the observed abundances in metal-poor stars or the solar r-process abundances.
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