Fuel & Fission
To make a nuclear reactor core, we need some magic rocks – nuclear fuel. We have a lot of elements and isotopes to pick from, but on Earth today, the most readily available nuclear fuel is uranium, specifically Uranium-235, or Uranium with 92 protons and 143 neutrons. These are good fuels compared to other heavy elements because they are relatively easy to break apart, and they also release plenty of neutrons we can then use to break up other atoms. More about that later.
It’s just a rock, usually in the form of an oxide, Uranium dioxide. Yellowcake is just a convenient form of various uranium oxides. You can buy some here. It’s also slightly radioactive. Some of the Uranium isotopes are decaying (or transforming) into other isotopes, releasing some radiation (or energy) in the process. Some of its atoms are also spontaneously breaking apart into smaller atoms and, in the process, releasing neutrons and other particles, also known as radiation. There are many ways for an isotope to decay such as emitting an electron (beta), alpha particles, neutrons, or gammas.
For a given sample, we can measure the emission rate and energy of these particles. The particle emission rate is known as the activity, measured in Bequerels (Bq = particles/s) or Curies (3.7 x 1010 particles/s). Dividing by the sample mass and correcting for the detector's sampling area, we can estimate the specific activity of the sample.
By itself, the activity is not very meaningful. For practical considerations of radiation damage and biological harm, we need to know what kind of particles are being emitted and with what energy. Together with some assumptions about how a target is exposed in terms of its distance, effective thickness, and time, we can then calculate the absorbed dose (energy/mass). We can then apply various biological weighting factors depending on the organs exposed and radiation sources to find the equivalent or effective dose, which is measured by Sieverts. Various complexities arise from how different elements and isotopes interact with biological and natural processes. For example, some isotopes can be ingested and passed through urine relatively quickly, posing little danger even if they have a high activity. Other isotopes might lodge themselves inside an organ for very long periods of time.
If you look more closely, you’ll notice that not all the Uranium atoms are the same, and they behave differently. These are the different isotopes of Uranium, having the same number of protons but a different number of neutrons. Natural uranium ore is made of 99.3% U-238 and 0.7% U-235 and a tiny bit of U-234. Due to differences in isotope decay half-lives and mechanisms, radioactivity in Uranium ore is 2.2% from U-235, 48.6% from uranium-238, and 49.2% from the trace amounts of uranium-234.
The isotopic abundance in natural uranium is a direct consequence of the history of the solar system and the universe. The uranium on Earth originates from super novae where energetically unfavorable r-process nuclear reactions turned iron into heavier elements including uranium and its parent isotopes, Pu-242 and Cm-247. It’s interesting to think that nuclear fission energy is a form of stored fusion energy that discharges on billion-year time scales. We can accelerate the energy release from the stardust by assembling a nuclear reactor. It’s pretty convenient for us humans given how difficult fusion energy may be to implement.
Both uranium isotopes decay into other elements relatively quickly compared to everyday materials. Uranium-235 has a decay half-life of 0.704 billion years, a bit shorter than U-238’s 4.468 billion years. As such, total Uranium and the U-235 fraction declines over time and there is less available today than in the past. This is unfortunate because while all the heavy atoms can be fissioned, it is much easier and practical to fission U-235 in a self-sustaining way, compared to the more stable U-238.
These decays produce about 40% of the Earth's total geothermal energy production of 44 TW. It is interesting to note that geothermal energy is just a form of nuclear decay energy. It drives plate tectonics and volcanic activity. Rerouting those energy flows could have interesting consequences for the Earth's geology, climate, and habitability. Today's human civilization consumes 18 TW of primary power and given the geographically limited distribution of geothermal resources, it is unlikely that geothermal energy would be the major contributor to human energy needs.
U-235 is special because it really likes to break apart and release nuclear energy when it gets hit by slow neutrons. U-235 is the nuclear fuel (fissile). In contrast, U-238 is more stable, and usually absorbs neutrons without releasing energy right away. When it does fission with fast neutrons, the neutrons collide inelastically with U-238, slowing to velocities that cannot cause further fissions in U-238. U-238 is not without its virtues, as it can capture neutrons and transform into Pu-239 which is more easily fissioned, similar to U-235. It is an effective neutron moderator or reflector by virtue of high inelastic reaction rates. It also has some beneficial neutron capture properties that improve the negative thermal feedback of a reactor, which we’ll get to later.
A Uranium fission in a nuclear reactor releases energy both instantaneously and after some time. Instantaneous energy release takes the form of kinetic energy carried away by the fission fragments and neutrons. That kinetic energy turns into thermal energy when the fragments interact with surrounding atoms. A small portion of the instantaneous energy release is contained in gamma rays that escape the core altogether.
The fission fragments are usually very unstable, having too few or too many neutrons, and will decay to more stable isotopes by various radioactive decay steps over the course of seconds, weeks, and years. The total energy that ends up as heat is roughly 202 MeV. About 8 MeV escape the reactor and Earth as anti-neutrinos.