# Nuclear fission **Nuclear fission** is the splitting of a heavy [[Atomic_nucleus|atomic nucleus]] into two lighter fragments, with two or three spare [[Neutron|neutrons]] and about 200 MeV of energy released in the process. It is a single event, and this page is about that single event: one ²³⁵[[Uranium|U]] nucleus absorbing one neutron and coming apart. What happens when the spare neutrons go on to split further nuclei is [[Nuclear_chain_reaction|the chain reaction]], and the machine built around a steady chain is [[Nuclear_reactor|the reactor]]; both are treated on their own pages and neither is restated here. In the microsim below the reader controls the split itself. One slider picks the light fragment's mass number A1 anywhere along the bimodal thermal yield curve — the one with humps near A = 95 and A = 140 rather than a peak at the symmetric split — and a second sets the number of spare neutrons.[^murphy-fission][^spec-p51] The energy released follows from a liquid-drop binding-energy table as `Q = BE(A1) + BE(A2) − BE(236)`, and the first surprise is how flat it is: wherever the reader puts the slider, Q lands near 200 MeV, because the binding-energy curve is nearly level across the whole fragment region.[^spec-p51][^murphy-be] A second panel shows where that energy goes, as the [[Coulomb's_law|Coulomb]] repulsion of the two charged fragments, `k·Z1·Z2·e²/(R1 + R2)` — an ILLUSTRATIVE figure at the scission point, not a measured one, and the page explains below exactly how far off it is and why. A third plots the fission barrier against `Z²/A`, the axis on which ²³⁵U and ²³⁸U sit only one percent apart and yet behave completely differently under a slow neutron.[^derived-nf] On the [[Physics]] flagship this article serves the *Fission* section of Part IV — Branches and fields. It is the Physics end of a seam the cluster draws deliberately: Physics owns the single splitting, [[Energy]] owns what happens when many of them are chained, and [[Nuclear_fuel_cycle|the fuel cycle]] owns where the ²³⁵U came from and where the fragments go. ## Physical overview Fission is rare among nuclear reactions in being violent enough to matter industrially and common enough to sustain itself. Only three nuclides fission readily on absorbing a slow neutron — ²³³U, ²³⁵U and ²³⁹[[Plutonium|Pu]] — and of those only ²³⁵U occurs in nature, at 0.72 % of natural uranium against 99.2745 % ²³⁸U.[^murphy-fission] That one isotope, in that small proportion, is the entire natural resource on which [[Nuclear_power|nuclear power]] rests. ### Mechanism A thermal neutron absorbed by ²³⁵U does not immediately split it. It forms a compound nucleus, ²³⁶U, in an excited state, and the excitation energy — supplied partly by the neutron's kinetic energy but mostly by the binding energy it releases on being captured — sets the nucleus oscillating between spherical and elongated shapes.[^os-nuclear][^krane] If the elongation carries the nucleus over its fission barrier, the two ends stop attracting and start repelling, the neck pinches, and the drop separates at a configuration called scission. If it does not, the excitation is radiated away as gamma rays and nothing happens. What comes out is not fixed. Murphy writes the canonical example as `²³⁵U + n → ⁹⁰Br + ¹⁴⁴La + 2n`, and the value of writing it out is the bookkeeping: 236 nucleons in, 236 out, and the two fragment charges must sum to 92.[^murphy-fission] Fix one fragment as bromine at Z = 35 and the partner must be lanthanum at Z = 57; the mass numbers then follow from the neutron count, ¹⁴⁶La if none escape and ¹⁴⁴La if two do.[^murphy-fission] The mass split is strongly asymmetric and reproducibly so: fragment masses cluster near A ≈ 95 and A ≈ 140, and the symmetric split near A = 118 is the *least* likely outcome, not the most.[^murphy-fission][^manual10] Typically two or three neutrons come free.[^murphy-fission] The sim therefore refuses to give a deterministic single outcome, because a deterministic single outcome misrepresents the physics.[^manual10] ### Energetics The energy comes from mass. Murphy's Table 15.7 balances the reaction at 236.05259 amu in and 235.86757 amu out, a defect of 0.18502 amu, which at 931.49432 MeV per amu is 172.3 MeV.[^murphy-energy] Ball's independent treatment, using a different fragment pair, gives a defect of 0.1834 g/mol and an energy of 1.65×10¹³ J per mole of reaction; dividing by Avogadro's number puts that at 171.0 MeV per fission, within 0.8 % of Murphy's figure from completely different fragments.[^ball][^derived-nf] That agreement is the real content of the sim's flat Q curve: the answer barely depends on how the nucleus divides. Almost all of it appears first as the [[Kinetic_energy|kinetic energy]] of two highly charged fragments flying apart, and this is where the sim's Coulomb panel has to be read carefully. Take A1 = 95 with Z1 = 36 and A2 = 139 with Z2 = 56. Using `R = 1.2·A^(1/3)`, the radii are 5.48 and 6.22 fm, and two such spheres just touching have a Coulomb energy of 248 MeV — more than the entire energy release.[^derived-nf] The excess is not an error in the arithmetic but a statement about the shape: at real scission the fragments are elongated, not spherical, and their centres are about 1.44 times further apart than touching spheres would be. The touching-sphere number is ILLUSTRATIVE, a display fit for the mechanism, and the page labels it as such. Per gram the numbers are extraordinary. Fission of ²³⁵U releases 16.8 million kcal/g against about 10 kcal/g for any chemical fuel, a factor near 1.7 million; per mole of reaction Ball's comparison is starker still, 1.65×10¹⁰ kJ/mol against roughly 650 kJ/mol for burning a CH₂ unit, a factor of 2.5×10⁷. The two ratios differ because one is per gram and the other per mole, and mixing them is the standard way to rank fusion and fission the wrong way round.[^murphy-energy][^ball][^manual05][^derived-nf] A person drawing 10 kW continuously for a year needs 3.155×10¹¹ J, which is 4.5 g of ²³⁵U.[^murphy-energy] ### Binding energy The reason fission pays at all is the shape of the [[Nuclear_binding_energy|binding energy]] per nucleon curve. It rises steeply from light nuclei, peaks near ⁵⁶[[Iron|Fe]] at 8.79 MeV per nucleon, and then falls slowly, reaching 7.59 MeV at ²³⁵U.[^murphy-be] Any process that moves nucleons toward the peak releases energy, so [[Nuclear_fusion|fusion]] pays below iron and fission pays above it.[^manual10] The obvious graphical estimate is instructive precisely because it is wrong. Reading the curve, ²³⁵U carries 7.6 × 235 = 1,790 MeV of binding; fragments at 8.7 × 95 and 8.4 × 140 carry 825 and 1,175 MeV, so the split appears to release about 210 MeV.[^murphy-be] The exact answer is 172 MeV. The gap has two causes: the estimate credits the fragments with binding they do not yet have, since they are born neutron-rich and highly excited, and it ignores the spare neutrons, which leave unbound.[^murphy-be] The difference eventually appears anyway, as the fragments [[Beta_decay|beta-decay]] toward stability over seconds to centuries — which is why ⁹⁰Sr and ¹³⁷Cs dominate the waste hazard from about five years out to a few hundred.[^murphy-energy] The same liquid-drop bookkeeping explains which nuclei fission easily. The barrier height falls as the fissility parameter `Z²/A` rises, and the actinides all sit near a barrier of order 6 MeV. But `Z²/A` alone cannot separate the two uranium isotopes: it is 36.0 for ²³⁵U and 35.6 for ²³⁸U, a difference of one percent against a difference of a thousand in thermal fission cross-section.[^derived-nf] What separates them is pairing. Capture on ²³⁵U completes a neutron pair and delivers roughly 6.5 MeV of excitation, above the barrier, so a neutron of any energy will do; capture on ²³⁸U leaves an unpaired neutron and delivers only about 4.8 MeV, below it, so ²³⁸U fissions only under a fast neutron carrying about an MeV of its own.[^krane] That is the whole reason [[Fissile_material|fissile]] and merely fissionable are different words. ### Chain reactions Because each fission frees two or three neutrons and consumes one, a population of fissions can sustain or grow itself. Ball develops the idea as pure doubling — one fission becoming 16,384 in fourteen generations — and stresses that criticality is a threshold rather than a linear effect: below it the population dies, above it the population runs away.[^ball] Everything quantitative about that threshold, from the multiplication factor to the [[Delayed_neutron|delayed neutrons]] that make it controllable, belongs to [[Nuclear_chain_reaction]] on the [[Energy]] spine and is not repeated here. ### Fission reactors A reactor is a machine for holding the chain exactly at break-even while extracting the heat. Its fuel is uranium [[Enriched_uranium|enriched]] to about 3–5 % ²³⁵U, low enough that the lattice only works with a moderator present, which is why a reactor core can melt but cannot explode like a bomb.[^murphy-energy][^ball] The reactor physics — moderation, the multiplication factor, control rods, kinetics — is the subject of [[Nuclear_reactor]], and the uranium supply chain that feeds it is [[Nuclear_fuel_cycle]]. ### Fission bombs A weapon inverts every design choice a reactor makes. It uses metal enriched to 70 % ²³⁵U or higher, assembles it fast and without a moderator so that neutrons stay fast and generations are short, and aims for the largest possible multiplication rather than break-even.[^ball][^murphy-energy] The engineering problem is holding the assembly together long enough for the chain to climb, since the same energy release blows it apart; that competition, and the [[Critical_mass|critical mass]] arithmetic behind it, is treated on [[Nuclear_chain_reaction]]. ## History Fission was found by chemists, not by physicists, and it was found by accident while looking for something else. The sequence from the first anomalous radiochemistry to a working pile took barely four years. ### Discovery of nuclear fission Through the 1930s several groups bombarded uranium with neutrons expecting to make heavier, transuranic elements. At the end of 1938 Otto Hahn and Fritz Strassmann, doing careful radiochemistry in Berlin, found instead that the product behaved chemically like barium — an element with barely half uranium's [[Atomic_number|atomic number]], which no known nuclear process could produce.[^rhodes] They published the chemistry without an interpretation. Lise Meitner and Otto Frisch supplied it within weeks, in the first days of 1939: the [[Semi-empirical_mass_formula|liquid drop]] had divided in two, and the energy released could be estimated straight from the mass defect and the Coulomb repulsion of the fragments.[^rhodes] The explanation and the first quantitative energy estimate arrived together, which is unusual and is part of why the result was accepted so quickly. ### Fission chain reaction realized Leó Szilárd had conceived a neutron-multiplying chain reaction in 1933, five years before any fission was observed, and patented it in 1934; what the idea lacked was a reaction releasing more neutrons than it consumed.[^rhodes] Fission supplied exactly that. The first controlled self-sustaining chain reaction was achieved on 2 December 1942 in a lattice of [[Graphite|graphite]] and natural uranium assembled under the stands of a stadium in Chicago — natural uranium being usable only because graphite is a good enough moderator to compensate for 0.72 % enrichment.[^rhodes][^murphy-fission] ### Manhattan Project and beyond The wartime programme that followed was overwhelmingly a separations problem rather than a physics problem: producing kilogram quantities of ²³⁵U from an isotope mixture that is chemically uniform, and producing ²³⁹Pu in reactors built for the purpose. Both routes were pursued to completion, and both devices built from them were used in 1945.[^rhodes] Civil power followed in the 1950s, and by 2019 the world fleet stood at 455 plants, 393 GW installed and about 295 GW average output, some 11 % of world electricity.[^murphy-energy] The [[Isotope_separation|separation]] problem never went away: it remains the reason enrichment capacity, rather than uranium ore, is the strategic quantity. ### Natural fission chain-reactors on Earth Nature ran the experiment first. At Oklo in Gabon, uranium ore bodies sustained fission chain reactions roughly 1.7 billion years ago, discovered in 1972 when ore from the deposit was found to be measurably depleted in ²³⁵U.[^oklo] The reason they could is arithmetic on two [[Half-life|half-lives]]. ²³⁵U decays with a half-life of 0.704 Gyr and ²³⁸U with 4.47 Gyr, so the lighter isotope has been vanishing about six times faster; running today's 0.72 % backwards 1.7 billion years gives about 2.9 %.[^murphy-energy][^derived-nf] That is the enrichment of modern reactor fuel, and at that level ordinary groundwater is a good enough moderator. The same arithmetic run further back puts the two isotopes at equal abundance some 6 billion years ago, before the Earth existed.[^murphy-energy] ## See also - [[Nuclear_fission_product]] — the bimodal fragment distribution the sim samples - [[Fissile_material]] - [[Semi-empirical_mass_formula]] — the liquid-drop table behind the sim's Q - [[Nuclear_chain_reaction]] — many fissions chained, on the Energy spine - [[Nuclear_reactor]] - [[Nuclear_binding_energy]] - [[Spontaneous_fission]] - [[Uranium]] ## References [^murphy-fission]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*, Chapter 15: only ²³³U, ²³⁵U and ²³⁹Pu are fissile and only ²³⁵U occurs naturally, p. 270; conservation of fragment charges and neutron numbers with Z₁ + Z₂ = 92, pp. 271–273; Eq. 15.2 `²³⁵U + n → ⁹⁰Br + ¹⁴⁴La + 2n` with 236 nucleons throughout, the typical 2–3 spare neutrons and the bimodal fragment masses near A ≈ 95 and ≈ 140, pp. 272–273; Example 15.4.1, the Br (Z = 35) / La (Z = 57) bookkeeping giving ¹⁴⁶La with no spare neutrons and ¹⁴⁴La with two, p. 272; natural uranium at 0.72 % ²³⁵U against 99.2745 % ²³⁸U, p. 277. https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet [^murphy-energy]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*, Chapter 15: Table 15.7, 236.05259 amu in and 235.86757 amu out for Δm = 0.18502 amu = 172.3 MeV, pp. 273–274; Box 15.3, 16.8×10⁶ kcal/g against ~10 kcal/g for chemical fuel, p. 274; Example 15.4.2, 3.155×10¹¹ J or 4.5 g of ²³⁵U per person-year at 10 kW, p. 274; the 2019 fleet at 455 plants, 393 GW installed, 295 GW average and 11 % of world electricity, p. 276; reactor fuel at 3–5 % ²³⁵U, weapons at ≥20 % and typically ~85 %, and depleted uranium at ≤0.3 %, pp. 277–278; the ²³⁵U and ²³⁸U half-lives of 0.704 Gyr and 4.47 Gyr and their equal abundance about 6 Gyr ago, p. 277; ⁹⁰Sr and ¹³⁷Cs dominating the waste hazard from ~5 to a few hundred years, p. 281; fuel that can melt down but cannot explode like a bomb, p. 282. https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet [^murphy-be]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*, Chapter 15: the binding-energy curve peaking near ⁵⁶Fe at 8.79 MeV per nucleon with ²³⁵U at 7.59, Table 15.5, pp. 267–269; and the graphical fission estimate — 7.6 × 235 = 1,790 MeV against 8.7 × 95 = 825 and 8.4 × 140 = 1,175 MeV, giving ≈210 MeV — together with the reasons it overestimates the exact 172 MeV, pp. 274–275. [^ball]: Ball, David (2011). *Introductory Chemistry*, Chapter on nuclear chemistry: `E = mc²` with Δm taken as products minus reactants, pp. 752–753; the ²³⁵U fission mass defect of 0.1834 g/mol and energy of 1.65×10¹³ J per mole of reaction, against ~650 kJ/mol per CH₂ unit in hydrocarbon combustion, pp. 752–753; the ²³⁸U case at −1.35×10¹³ J, pp. 755–756; the chain reaction developed as doubling, one fission to 16,384 in fourteen generations, and the thresholds for natural uranium at 0.7 %, reactor fuel at ~3 % and weapons at ≥70 %, p. 757; and the warning that criticality is a threshold rather than a linear effect. https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry [^os-nuclear]: OpenStax (Sanny, Jeff; Ling, Samuel, eds.) (2016). *University Physics Volume 3*, Chapter 10 *Nuclear Physics*, pp. 441–492 (page to pin): neutron capture forming an excited compound nucleus, the deformation-to-scission picture of fission, and the nuclear radius rule `R = r0·A^(1/3)` with r0 ≈ 1.2 fm used in the Coulomb estimate here. https://openstax.org/details/books/university-physics-volume-3 [^krane]: Krane, Kenneth S. *Introductory Nuclear Physics* (Wiley, 1988), chapters on nuclear models and fission (pages to pin): the liquid-drop fission barrier and its dependence on the fissility parameter `Z²/A`; the actinide barrier of order 6 MeV; and the even–odd pairing argument by which neutron capture on ²³⁵U delivers roughly 6.5 MeV of excitation, above the barrier, while capture on ²³⁸U delivers only about 4.8 MeV, below it, so that ²³⁸U requires a fast neutron of order 1 MeV. No Portal Book in this cluster treats the fission barrier or the pairing term, so these are cited to a standard text rather than assigned Portal Book pages. [^rhodes]: Rhodes, Richard. *The Making of the Atomic Bomb* (Simon & Schuster, 1986), pages to pin: the 1930s transuranic searches; the Hahn–Strassmann radiochemistry of December 1938 identifying barium among the products; the Meitner–Frisch interpretation and energy estimate of January 1939; Szilárd's 1933 conception and 1934 patent of a neutron chain reaction; the first self-sustaining chain reaction of 2 December 1942 in a graphite and natural-uranium lattice; and the wartime separation and plutonium-production programmes. [^oklo]: International Atomic Energy Agency, material on the *Oklo natural fission reactors*, Gabon (page to pin): the anomalous ²³⁵U depletion identified in 1972 and the reactor episodes dated to approximately 1.7 billion years ago. No Portal Book covers Oklo. [^manual10]: Wikitube MicroSim Guide, sub-manual 10 *Earth, Energy and Environment*, §4.3 "U-235 fission: fragments, spare neutrons and the chain reaction" and §4.2 "Binding energy per nucleon": the bimodal fragment distribution and the requirement that a sim sample it rather than fix one outcome, since a deterministic single outcome misrepresents the physics; the instruction to conserve Z and N including spare neutrons; and the statement that fusion pays on the low-A side of the binding-energy peak and fission on the high-A side. [^manual05]: Wikitube MicroSim Guide, sub-manual 05 *Chemistry*, §9.3 "Mass defect to energy: fission, fusion and chemistry": the mass-defect-to-energy microsim and its preset ladder from the H–H bond through CH₂ combustion to D + T and ²³⁵U, with the pitfalls that the book prints released energy as negative and that per-mole and per-gram comparisons rank fusion and fission in opposite orders. [^spec-p51]: Matter & Energy Cluster contract, `_registry/plans/PHYSICS_SECTIONS.md` row P51: the sim concept for this page — the reader picks the light fragment's mass A1 on the bimodal yield curve and the number of spare neutrons; `Q = BE(A1) + BE(A2) − BE(236)` read from a semi-empirical-mass-formula table lands near 200 MeV whatever the split; the fragment Coulomb repulsion `k·Z1·Z2·e²/(R1 + R2)` is marked ILLUSTRATIVE at scission; the fission barrier is plotted against `Z²/A`; and the chain reaction, k_eff and the reactor are explicitly assigned to the Energy spine at row P52 rather than to this page. [^derived-nf]: Computed for this article from the equations and constants cited above, with `k·e² = 1.43996 MeV·fm`: Ball's 1.65×10¹³ J per mole divided by 6.022×10²³ is 2.740×10⁻¹¹ J = 171.0 MeV per fission, 0.8 % below Murphy's 172.3 MeV from a different fragment pair; for A1 = 95 (Z = 36) and A2 = 139 (Z = 56), `R1 = 1.2 × 95^(1/3) = 5.48 fm` and `R2 = 1.2 × 139^(1/3) = 6.22 fm`, so two touching spheres carry `1.43996 × 36 × 56 / 11.70 = 248 MeV`, and matching the 172.3 MeV release instead requires a centre separation of 16.85 fm, a factor of 1.44 beyond touching; the fissility parameters `Z²/A` of 36.02 for ²³⁵U, 35.86 for ²³⁶U, 35.56 for ²³⁸U and 36.97 for ²³⁹Pu; the energy-density ratios 16.8×10⁶ ÷ 10 = 1.7×10⁶ per gram and 1.65×10¹⁰ ÷ 650 = 2.5×10⁷ per mole; and the Oklo enrichment `0.00725 × 2^(1.7/0.704 − 1.7/4.47) = 0.0297`, i.e. 2.9 % ²³⁵U at 1.7 Ga. ## Further reading - Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*, Chapter 15. CC BY-NC. The mass-defect bookkeeping, Table 15.7 and the fuel arithmetic used throughout this page. - Ball, David (2011). *Introductory Chemistry*, nuclear chemistry chapter. CC BY-NC-SA. The independent per-mole calculation that cross-checks Murphy's per-fission energy. - OpenStax (2016). *University Physics Volume 3*, Chapter 10 *Nuclear Physics*. CC BY. The compound-nucleus and nuclear-size treatment. - Krane, Kenneth S. (1988). *Introductory Nuclear Physics*, Wiley. The standard text for the fission barrier, the fissility parameter and the pairing argument. ## External links - [*Energy and Human Ambitions on a Finite Planet*](https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet) (Murphy, 2021), Chapter 15 - [*Introductory Chemistry*](https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry) (Ball, 2011) — the mass-defect worked examples - [*University Physics Volume 3*](https://openstax.org/details/books/university-physics-volume-3) (OpenStax, 2016), Chapter 10 - The Wikipedia pair's *External links* section lists the evaluated nuclear-data libraries from which measured fission-product yields and cross-sections are taken. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Nuclear_fission.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Nuclear fission* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Nuclear_fission.html" data-title="Nuclear fission"></div> *Built from `MICROSIM_GUIDE/specs/sims/Nuclear_fission.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Nuclear_fission) : [Wikitube](https://en.wikitube.io/wiki/Nuclear_fission) · pinned revision [1369434153](https://en.wikipedia.org/w/index.php?oldid=1369434153) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Physics]], [[PORTAL_Energy]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Physics row P51 · sim pending (matter/Nuclear_fission).*