Each nucleus, consisting of protons and neutrons (collectively known as nucleons), has an associated binding energy. A graph of binding energy per nucleon is shown in the graph below. The total binding energy of a nucleus is the energy released when a nucleus is assembled from individual nucleons; the greater the energy release, the lower the potential energy of the nucleus, so higher binding energy in the graph represents greater stability. When one nucleus is converted to another or others of higher binding energy, whether that be through a natural radioactive process or through an artificially induced process, the difference in the total binding energies of the nuclei is released as kinetic energy of the particles produced and gamma rays. This energy can be harnessed through traditional methods, e.g. by heating water to generate steam to drive a turbine, and so electricity can be produced.
Origins of Binding Energy
The measured binding energies of the nuclides can be fitted reasonably well by Weizsäcker’s formula (see below). The formula is derived by treating the nucleus as analogous to a liquid drop, with surface energy and volume energy terms leading to the two dominant contributions: a term proportional to A, the atomic mass and to the volume of the nucleus, and a term proportional to -A2/3 due to the surface energy. These two terms compete, much in the same way they do in other processes (e.g. nucleation), facilitating a qualitative understanding of why nuclei split up or join together under certain conditions.
Energy is given off when a nucleus becomes more stable, i.e. approaches the maximum on the graph above. Moving from lighter nuclei towards this maximum requires two nuclei to combine and form a heavier one (fusion), whereas moving from heavier nuclei towards this maximum requires the nucleus to split apart (fission). The energy release per mass of nuclide is much higher for fusion than for fission. Fusion has many other attractive attributes as a basis for power generation, but since nuclei are positively charged, sufficient energy most be put into the system to overcome the repulsion between nuclei so that a fusion process can occur. This Coulomb barrier can also be expressed as an ignition temperature. The technical challenges are many, and nothing close to a commercially viable reactor currently exists. Fusion for power generation is still a prominent research topic, and experimental reactors are in the process of being built, such as ITER (International Thermonuclear Experimental Reactor), which is planned to be completed by 2018.
Since nuclear fusion is not yet a practical power source, this TLP will instead focus on nuclear fission as means to generate heat and electricity.
Nuclear fission, as previously mentioned, involves splitting a heavier nucleus into two lighter nuclei. Fission can be induced if a nucleus absorbs a neutron of sufficient energy. If a nucleus undergoes fission regardless of the incident neutron energy, the nucleus is referred to as fissile; otherwise, if there is a threshold energy then the nucleus is referred to as fissionable.
Examples of fissile nuclides include 233U, 235U and 239Pu. The nuclide most commonly used in nuclear reactors is 235U.
A neutron will not necessarily induce fission if it passes through the nucleus. For example, fast neutrons are less likely to induce fission in 235U than thermal neutrons (i.e. neutrons with kinetic energy of the order of kT). Qualitatively, this makes sense since the faster a neutron is travelling the less time it spends inside the nucleus and so the less opportunity it has to induce fission within the nucleus. The actual reasons for this are complicated, and this topic is explored further on the “Cross Sections” page.
Fissionable nuclides, such as 238U and 239Pu, are also used in so-called “fast” reactors, where the neutrons are travelling fast enough (commonly around 10% the speed of light, or 1 MeV) to overcome the activation energy required to make fissionable nuclides decay.
The movie below illustrates the fission process:
As can be seen in the movie, the parent nucleus decays into two fission fragments of unequal mass with a combined kinetic energy of about 169 MeV and several neutrons with a kinetic energy of about 2 MeV each (for 235U, the average number of neutrons produced is 2.4, but can be as high as 5). These neutrons are highly energetic, with 7–8 orders of magnitude more energy than thermalized neutrons. A gamma ray of about 7 MeV is also released. The neutrons could induce further fission events in other nuclei and thus cause a chain reaction, but in practice they are too fast and must first be slowed down inside the reactor.
The nuclides produced by fission are usually of unequal mass, as shown in the graph above. The x-axis of the graph is by atomic mass, not atomic number. Many fission fragments are highly unstable, and decay by giving off beta radiation: this involves a neutron changing into a proton within the nucleus, leaving the overall number of nucleons (and hence the mass of the nucleus) the same.
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