Editing Nuclear fission (section)

===Energetics===

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[[File:Stdef2.png|150px|right|thumb|The stages of binary fission in a liquid drop model. Energy input deforms the nucleus into a fat "cigar" shape, then a "peanut" shape, followed by binary fission as the two lobes exceed the short-range [[nuclear force]] attraction distance, and are then pushed apart and away by their electrical charge. In the liquid drop model, the two fission fragments are predicted to be the same size. The nuclear shell model allows for them to differ in size, as usually experimentally observed.]]

Fission [[Nuclear cross section|cross sections]] are a measurable property related to the probability that fission will occur in a nuclear reaction. Cross sections are a function of incident neutron energy, and those for {{chem|235|U}} and {{chem|239|Pu}} are a million times higher than {{chem|238|U}} at lower neutron energy levels. Absorption of any neutron makes available to the nucleus binding energy of about 5.3&nbsp;MeV. {{chem|238|U}} needs a fast neutron to supply the additional 1&nbsp;MeV needed to cross the critical energy barrier for fission. In the case of {{chem|235|U}} however, that extra energy is provided when {{chem|235|U}} adjusts from an odd to an even mass. In the words of Younes and Lovelace, "...the neutron absorption on a {{chem|235|U}} target forms a {{chem|236|U}} nucleus with excitation energy greater than the critical fission energy, whereas in the case of ''n'' + {{chem|238|U}}, the resulting {{chem|239|U}} nucleus has an excitation energy below the critical fission energy."<ref name=ww/>{{rp|25–28}}<ref name=rr/>{{rp|282–287}}<ref>{{cite journal |last1=Bohr |first1=N. |title=Resonance in Uranium and Thorium Disintegrations and the Phenomenon of Nuclear Fission |url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.55.418.2 |journal=Physical Review |publisher=American Physical Society |access-date=9 October 2023 |date=1939|volume=55 |issue=4 |pages=418–419 |doi=10.1103/PhysRev.55.418.2 |bibcode=1939PhRv...55..418B }}</ref><ref>{{cite web |title=Essential cross sections |url=https://eng.libretexts.org/Sandboxes/jhalpern/Energy_Alternatives/04%3A_Nuclear_Power/4.06%3A_Controlling_the_Fission_Chain_Reaction-_Nuclear_Reactors/4.6.01%3A_Essential_Cross_Sections |website=LibreTexts Library |date=July 2022 |access-date=9 October 2023}}</ref>

About 6&nbsp;MeV of the fission-input energy is supplied by the simple binding of an extra neutron to the heavy nucleus via the strong force; however, in many fissionable isotopes, this amount of energy is not enough for fission. Uranium-238, for example, has a near-zero fission cross section for neutrons of less than 1&nbsp;MeV energy. If no additional energy is supplied by any other mechanism, the nucleus will not fission, but will merely absorb the neutron, as happens when {{chem|238|U}} absorbs slow and even some fraction of fast neutrons, to become {{chem|239|U}}. The remaining energy to initiate fission can be supplied by two other mechanisms: one of these is more kinetic energy of the incoming neutron, which is increasingly able to fission a [[fissionable]] heavy nucleus as it exceeds a kinetic energy of 1&nbsp;MeV or more (so-called fast neutrons). Such high energy neutrons are able to fission {{chem|238|U}} directly (see [[thermonuclear weapon]] for application, where the fast neutrons are supplied by nuclear fusion). However, this process cannot happen to a great extent in a nuclear reactor, as too small a fraction of the fission neutrons produced by any type of fission have enough energy to efficiently fission {{chem|238|U}}. (For example, neutrons from thermal fission of {{chem|235|U}} have a [[mean]] energy of 2&nbsp;MeV, a [[median]] energy of 1.6&nbsp;MeV, and a [[mode (statistics)|mode]] of 0.75&nbsp;MeV,<ref>{{cite book |last1=Byrne |first1=James |title=Neutrons, nuclei, and matter: an exploration of the physics of slow neutrons |url=https://books.google.com/books?id=njUjm4Rkg9UC&pg=PA259 |date=2011 |publisher=Dover Publications |location=Mineola, N.Y |isbn=978-0-486-48238-5 |edition=Dover |page=259}}</ref><ref>{{cite journal |last1=Kauffman |first1=Andrew |last2=Herminghuysen |first2=Kevin |last3=Van Zile |first3=Matthew |last4=White |first4=Susan |last5=Hatch |first5=Joel |last6=Maier |first6=Andrew |last7=Cao |first7=Lei R. |title=Review of research and capabilities of 500 kW research reactor at the Ohio State University |journal=Annals of Nuclear Energy |date=October 2024 |volume=206 |doi=10.1016/j.anucene.2024.110647 |quote=Consequently, the fast neutron energy spectrum of FBF is at above 0.4 eV, with an average of 2.0 MeV and the median energy of 1.6 MeV.|doi-access=free |bibcode=2024AnNuE.20610647K }}</ref> and the energy spectrum for fast fission is similar.{{citation needed|date=November 2024}})

Among the heavy [[actinide]] elements, however, those isotopes that have an odd number of neutrons (such as <sup>235</sup>U with 143 neutrons) bind an extra neutron with an additional 1 to 2&nbsp;MeV of energy over an isotope of the same element with an even number of neutrons (such as <sup>238</sup>U with 146 neutrons). This extra binding energy is made available as a result of the mechanism of [[Semi-empirical mass formula#Pairing term|neutron pairing effects]], which itself is caused by the [[Pauli exclusion principle]], allowing an extra neutron to occupy the same nuclear orbital as the last neutron in the nucleus. In such isotopes, therefore, no neutron kinetic energy is needed, for all the necessary energy is supplied by absorption of any neutron, either of the slow or fast variety (the former are used in moderated nuclear reactors, and the latter are used in [[fast-neutron reactor]]s, and in weapons).

According to Younes and Loveland, "Actinides like {{chem|235|U}} that fission easily following the absorption of a thermal (0.25 meV) neutron are called ''fissile'', whereas those like {{chem|238|U}} that do not easily fission when they absorb a thermal neutron are called ''fissionable''."<ref name=ww/>{{rp|25}}

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After an incident particle has fused with a parent nucleus, if the excitation energy is sufficient, the nucleus breaks into fragments. This is called scission, and occurs at about 10<sup>−20</sup> seconds. The fragments can emit prompt neutrons at between 10<sup>−18</sup> and 10<sup>−15</sup> seconds. At about 10<sup>−11</sup> seconds, the fragments can emit gamma rays. At 10<sup>−3</sup> seconds β decay, β-[[delayed neutron]]s, and gamma rays are emitted from the [[decay product]]s.<ref name=ww/>{{rp|23–24}}

Typical fission events release about two hundred million [[electronvolt|eV]] (200&nbsp;MeV) of energy for each fission event. The exact isotope which is fissioned, and whether or not it is fissionable or fissile, has only a small impact on the amount of energy released. This can be easily seen by examining the curve of [[binding energy]] (image below), and noting that the average binding energy of the actinide nuclides beginning with uranium is around 7.6&nbsp;MeV per nucleon. Looking further left on the curve of binding energy, where the fission products cluster, it is easily observed that the binding energy of the fission products tends to center around 8.5&nbsp;MeV per nucleon. Thus, in any fission event of an isotope in the actinide mass range, roughly 0.9&nbsp;MeV are released per nucleon of the starting element. The fission of <sup>235</sup>U by a slow neutron yields nearly identical energy to the fission of <sup>238</sup>U by a fast neutron. This energy release profile holds for thorium and the various minor actinides as well.<ref name=ENS>{{cite web |author=Marion Brünglinghaus |url=http://www.euronuclear.org/info/encyclopedia/n/nuclear-fission.htm |title=Nuclear fission |publisher=European Nuclear Society |access-date=2013-01-04 |archive-url=https://web.archive.org/web/20130117002723/http://www.euronuclear.org/info/encyclopedia/n/nuclear-fission.htm |archive-date=2013-01-17 |url-status=dead }}</ref>

[[File:Bucky1.gif|thumb|right|Animation of a [[Coulomb explosion]] in the case of a cluster of positively charged nuclei, akin to a cluster of fission fragments. [[Hue]] level of color is proportional to (larger) nuclei charge. Electrons (smaller) on this time-scale are seen only stroboscopically and the hue level is their kinetic energy.]]
When a [[uranium]] nucleus fissions into two daughter nuclei fragments, about 0.1 percent of the mass of the uranium nucleus<ref name="bulletin1950">Hans A. Bethe (April 1950), [https://books.google.com/books?id=Mg4AAAAAMBAJ&pg=PA99 "The Hydrogen Bomb"], ''Bulletin of the Atomic Scientists'', p. 99.</ref> appears as the fission energy of ~200&nbsp;MeV. For uranium-235 (total mean fission energy 202.79&nbsp;MeV<ref name="KopMikSin2004">{{cite journal |arxiv=hep-ph/0410100 |doi=10.1134/1.1811196 |last1=V |first1=Kopeikin |last2=L |first2=Mikaelyan and |last3=V |first3=Sinev |title=Reactor as a Source of Antineutrinos: Thermal Fission Energy |journal=Physics of Atomic Nuclei |volume=67 |issue=10 |page=1892 |year=2004|bibcode=2004PAN....67.1892K |s2cid=18521811 }}</ref>), typically ~169&nbsp;MeV appears as the kinetic energy of the daughter nuclei, which fly apart at about 3% of the speed of light, due to [[Coulomb's law|Coulomb repulsion]]. Also, an average of 2.5&nbsp;neutrons are emitted, with a [[mean]] kinetic energy per neutron of ~2&nbsp;MeV (total of 4.8&nbsp;MeV).<ref>These fission neutrons have a wide energy spectrum, ranging from 0 to 14&nbsp;MeV, with a mean of 2&nbsp;MeV and a [[mode (statistics)|mode]] of 0.75&nbsp;MeV. See Byrne, op. cite.</ref> The fission reaction also releases ~7&nbsp;MeV in prompt gamma ray [[photon]]s. The latter figure means that a nuclear fission explosion or criticality accident emits about 3.5% of its energy as gamma rays, less than 2.5% of its energy as fast neutrons (total of both types of radiation ~6%), and the rest as kinetic energy of fission fragments (this appears almost immediately when the fragments impact surrounding matter, as simple heat).<ref>{{cite web |url = https://ke.army.mil/bordeninstitute/published_volumes/nuclearwarfare/chapter1/chapter1.pdf |title = NUCLEAR EVENTS AND THEIR CONSEQUENCES by the Borden institute..."approximately '''82%''' of the fission energy is released as kinetic energy of the two large fission fragments. These fragments, being massive '''and highly charged particles''', interact readily with matter. They transfer their energy quickly to the surrounding weapon materials, which rapidly become heated" |archive-url=https://web.archive.org/web/20170125171152/https://ke.army.mil/bordeninstitute/published_volumes/nuclearwarfare/chapter1/chapter1.pdf |archive-date=25 January 2017 |url-status=dead}}</ref><ref>{{cite web |url=http://www.oektg.at/wp-content/uploads/02-Nuclear-Engineering-Overview1.pdf |archive-url=https://web.archive.org/web/20180515201022/http://www.oektg.at/wp-content/uploads/02-Nuclear-Engineering-Overview1.pdf |title=''Nuclear Engineering Overview'' The various energies emitted per fission event pg 4. ''"167&nbsp;MeV"'' is emitted by means of the repulsive electrostatic energy between the 2 daughter nuclei, which takes the form of the "kinetic energy" of the fission products, this kinetic energy results in both later blast and thermal effects. ''"5&nbsp;MeV"'' is released in prompt or initial gamma radiation, ''"5&nbsp;MeV"'' in prompt neutron radiation (99.36% of total), ''"7&nbsp;MeV"'' in delayed neutron energy (0.64%) and ''"13&nbsp;MeV"'' in beta decay and gamma decay(residual radiation) |archive-date=May 15, 2018 |publisher=Technical University Vienna }}</ref>

Some processes involving neutrons are notable for absorbing or finally yielding energy — for example neutron kinetic energy does not yield heat immediately if the neutron is captured by a uranium-238 atom to breed plutonium-239, but this energy is emitted if the plutonium-239 is later fissioned. On the other hand, so-called [[delayed neutrons]] emitted as radioactive decay products with half-lives up to several minutes, from fission-daughters, are very important to [[nuclear reactor physics|reactor control]], because they give a characteristic "reaction" time for the total nuclear reaction to double in size, if the reaction is run in a "[[delayed criticality|delayed-critical]]" zone which deliberately relies on these neutrons for a supercritical chain-reaction (one in which each fission cycle yields more neutrons than it absorbs). Without their existence, the nuclear chain-reaction would be [[prompt critical]] and increase in size faster than it could be controlled by human intervention. In this case, the first experimental atomic reactors would have run away to a dangerous and messy "prompt critical reaction" before their operators could have manually shut them down (for this reason, designer [[Enrico Fermi]] included radiation-counter-triggered control rods, suspended by electromagnets, which could automatically drop into the center of [[Chicago Pile-1]]). If these delayed neutrons are captured without producing fissions, they produce heat as well.<ref>{{cite web|url=http://www.kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_7/4_7_1.html|title=Nuclear Fission and Fusion, and Nuclear Interactions|publisher=National Physical Laboratory|access-date=2013-01-04|archive-url=https://web.archive.org/web/20100305114800/http://www.kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_7/4_7_1.html|archive-date=2010-03-05|url-status=dead}}</ref>