Nuclear fission

Younes and Loveland define fission as, "...a collective motion of the protons and neutrons that make up the nucleus, and as such it is distinguishable from other phenomena that break up the nucleus. Nuclear fission is an extreme example of large-amplitude collective motion that results in the division of a parent nucleus into two or more fragment nuclei. The fission process can occur spontaneously, or it can be induced by an incident particle." Most of the energy from fission, about 85 percent, is found in fragment kinetic energy, while about 6 percent each comes from initial neutrons and gamma rays, then Beta decay neutrons and gamma rays, plus about 3 percent from β decay neutrinos.[4]^{: 21–22, 30}

A visual representation of an induced nuclear fission event where a slow-moving neutron is absorbed by the nucleus of a uranium-235 atom, which fissions into two fast-moving lighter elements (fission products) and additional neutrons. Most of the energy released is in the form of the kinetic velocities of the fission products and the neutrons.

Fission product yields by mass for thermal neutron fission of uranium-235, plutonium-239, a combination of the two typical of current nuclear power reactors, and uranium-233 used in the thorium cycle.

Nuclear fission can occur without neutron bombardment as a type of radioactive decay. This type of fission is called spontaneous fission, and was first observed in 1940.[4]^: 22

During induced fission, a compound system is formed after an incident particle fuses with a target. The resultant excitation energy may be sufficient to emit neutrons, or gamma-rays, and nuclear scission. Fission into two fragments, binary fission, is the most common nuclear reaction. Occurring least frequently is ternary fission, in which a third particle is emitted. This third particle is commonly an α particle.[4]^: 21–24 Since in nuclear fission, the nucleus emits more neutrons than the one it absorbs, a chain reaction is possible.[5]^{: 291, 296}

The most common fission process is binary fission, and it produces the fission products noted above, at 95±15 and 135±15 u. However, the binary process happens merely because it is the most probable. In anywhere from 2 to 4 fissions per 1000 in a nuclear reactor, a process called ternary fission produces three positively charged fragments (plus neutrons) and the smallest of these may range from so small a charge and mass as a proton (Z = 1), to as large a fragment as argon (Z = 18). The most common small fragments, however, are composed of 90% helium-4 nuclei with more energy than alpha particles from alpha decay (so-called "long range alphas" at ~ 16 MeV), plus helium-6 nuclei, and tritons (the nuclei of tritium). The ternary process is less common, but still ends up producing significant helium-4 and tritium gas buildup in the fuel rods of modern nuclear reactors.[6]

Bohr and Wheeler used their liquid drop model, the packing fraction curve of Arthur Jeffrey Dempster, and Eugene Feenberg's estimates of nucleus radius and surface tension, to estimate the mass differences of parent and daughters in fission. They then equated this mass difference to energy using Einstein's mass-energy equivalence formula. The stimulation of the nucleus after neutron bombardment was analogous to the vibrations of a liquid drop, with surface tension and the Coulomb force in opposition. Plotting the sum of these two energies as a function of elongated shape, they determined the resultant energy surface had a saddle shape. The saddle provided an energy barrier called the critical energy barrier. Energy of about 6 MeV provided by the incident neutron was necessary to overcome this barrier and cause the nucleus to fission.[4]^: 10–11[7][8] According to John Lilley, "The energy required to overcome the barrier to fission is called the activation energy or fission barrier and is about 6 MeV for A~240. It is found that the activation energy decreases as A increases. Eventually, a point is reached where activation energy disappears altogether...it would undergo very rapid spontaneous fission."[9]

Maria Goeppert Mayer later proposed the nuclear shell model for the nucleus. The chemical element isotopes that can sustain a fission chain reaction are called nuclear fuels, and are said to be 'fissile'. The most common nuclear fuels are ²³⁵U (the isotope of uranium with mass number 235 and of use in nuclear reactors) and ²³⁹Pu (the isotope of plutonium with mass number 239). These fuels break apart into a bimodal range of chemical elements with atomic masses centering near 95 and 135 u (fission products). Most nuclear fuels undergo spontaneous fission only very slowly, decaying instead mainly via an alpha-beta decay chain over periods of millennia to eons. In a nuclear reactor or nuclear weapon, the overwhelming majority of fission events are induced by bombardment with another particle, a neutron, which is itself produced by prior fission events.

Fissionable isotopes such as uranium-238 require additional energy provided by fast neutrons (such as those produced by nuclear fusion in thermonuclear weapons). While some of the neutrons released from the fission of ²³⁸
U are fast enough to induce another fission in ²³⁸
U, most are not, meaning it can never achieve criticality. While there is a very small (albeit nonzero) chance of a thermal neutron inducing fission in ²³⁸
U, neutron absorption is orders of magnitude more likely.

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, then are 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 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 U-235 and Pu-239 are a million times higher than U-238 at lower neutron energy levels. Absorption of any neutron makes available to the nucleus binding energy of about 5.3 MeV. U238 needs a fast neutron to supply the additional 1 MeV needed to cross the critical energy barrier for fission. In the case of U235 however, that extra energy is provided when U235 adjusts from an odd to an even mass. In the words of Younes and Lovelace, "...the neutron absorption on a ²³⁵
U target forms a ²³⁶
U nucleus with excitation energy greater than the critical fission energy, whereas in the case of n + ²³⁸
U, the resulting ²³⁹
U nucleus has an excitation energy below the critical fission energy."[4]^: 25–28[5]^{: 282–287}[10][11]

About 6 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 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 ²³⁸U absorbs slow and even some fraction of fast neutrons, to become ²³⁹U. 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 MeV or more (so-called fast neutrons). Such high energy neutrons are able to fission ²³⁸U 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 ²³⁸U (fission neutrons have a mode energy of 2 MeV, but a median of only 0.75 MeV, meaning half of them have less than this insufficient energy).[12]

Among the heavy actinide elements, however, those isotopes that have an odd number of neutrons (such as ²³⁵U with 143 neutrons) bind an extra neutron with an additional 1 to 2 MeV of energy over an isotope of the same element with an even number of neutrons (such as ²³⁸U with 146 neutrons). This extra binding energy is made available as a result of the mechanism of neutron pairing effects. This extra energy results from the Pauli exclusion principle allowing an extra neutron to occupy the same nuclear orbital as the last neutron in the nucleus, so that the two form a pair. 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 reactors, and in weapons).

According to Younes and Loveland, "Actinides like ²³⁵
U that fission easily following the absorption of a thermal (0.25 meV) neutron are called fissile, whereas those like ²³⁸
U that do not easily fission when they absorb a thermal neutron are called fissionable."[4]^: 25.

After an incidient 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^-20 seconds. The fragments can emit prompt neutrons at between 10^-18 and 10^-15 seconds. At about 10^-11 seconds, the fragments can emit gamma rays. At 10^-3 seconds β decay, β-delayed neutrons, and gamma rays are emitted from the decay products.[4]^: 23–24

Typical fission events release about two hundred million eV (200 MeV) of energy, the equivalent of roughly >2 trillion kelvin, 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 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 MeV per nucleon. Thus, in any fission event of an isotope in the actinide mass range, roughly 0.9 MeV are released per nucleon of the starting element. The fission of ²³⁵U by a slow neutron yields nearly identical energy to the fission of ²³⁸U by a fast neutron. This energy release profile holds true for thorium and the various minor actinides as well.[13]

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[14] appears as the fission energy of ~200 MeV. For uranium-235 (total mean fission energy 202.79 MeV[15]), typically ~169 MeV appears as the kinetic energy of the daughter nuclei, which fly apart at about 3% of the speed of light, due to Coulomb repulsion. Also, an average of 2.5 neutrons are emitted, with a mean kinetic energy per neutron of ~2 MeV (total of 4.8 MeV).[16] The fission reaction also releases ~7 MeV in prompt gamma ray photons. 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).[17][18]

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 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-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.[19]

The "curve of binding energy": A graph of binding energy per nucleon of common isotopes.

The binding energy of the nucleus is the difference between the rest-mass energy of the nucleus and the rest-mass energy of the neutron and proton nucleons. The binding energy formula includes volume, surface and Coulomb energy terms that include empirically derived coefficients for all three, plus energy ratios of a deformed nucleus relative to a spherical form for the surface and Coulomb terms. Additional terms can be included such as symmetry, pairing, the finite range of the nuclear force, and charge distribution within the nuclei to improve the estimate.[4]^: 46–50 Normally binding energy is referred and plotted as average binding energy per nucleon.[9]

According to Lilley, "The binding energy of a nucleus B is the energy required to separate it into its constituent neutrons and protons."[9]

$${\displaystyle m(\mathbf {A} ,\mathbf {Z} )=\mathbf {Z} m_{H}+\mathbf {N} m_{n}-\mathbf {B} /c^{2}}$$

where A is mass number, Z is atomic number, m_H is the atomic mass of a hydrogen atom, m_n is the mass of a neutron, and c is the speed of light. Thus, the mass of an atom is less than the mass of its constituent protons and neutrons, and assuming the average binding energy of its electrons is negligible. The binding energy B is expressed in energy units, using Einstein's mass-energy equivalence relationship. The binding energy also provide s an estimate of the total energy released from fission.[9]

The curve of binding energy is characterized by a broad maximum near mass number 60 at 8.6 MeV, then gradually decreases to 7.6 MeV at the highest mass numbers. Mass numbers higher than 238 are rare. At the lighter end of the scale, peaks are noted for helium-4, and the multiples such as beryllium-8, Carbon-12, oxygen-16, neon-20 and magnesium-24. Binding energy due to the nuclear force approaches a constatnt value for large A, while the Coulomb acts over a larger distance so that electrical potential energy per proton grows as Z increases. Fission energy is released when a A larger than 120 nucleus fragments. Fusion energy is released when lighter nuclei combine.[9]

Carl Friedrich von Weizsäcker's semi-empirical mass formula may be used to express the binding energy as the sum of five terms that includes volume energy, a surface correction, Coulomb energy, a symmetry term, and a pairing term:[9]

$${\displaystyle B=a_{v}\mathbf {A} -a_{s}\mathbf {A} ^{2/3}-a_{c}{\frac {\mathbf {Z} ^{2}}{\mathbf {A} ^{1/3}}}-a_{a}{\frac {(\mathbf {N} -\mathbf {Z} )^{2}}{\mathbf {A} }}\pm \Delta }$$

where the nuclear binding energy is proportional to the nuclear volume, while nucleons near the surface interact with fewer nucleons reduces the effect of the volume term. According to Lilley, "For all naturally occurring nuclei, the surface-energy term dominates and the nucleus exists in a state of equilibrium." The negative contribution of Coulomb energy arises from the repulsive electric force of the protons. The symmetry term arises from the fact that effective forces in the nucleus is stronger for unlike neutron-proton pairs, rather than like neutron-neutron or proton-proton pairs. The pairing term arises from the fact that like nucleons form spin-zero pairs in the same spatial state. The pairing is positive if N and Z are both even, adding to the binding energy.[9]

In fission there is a preference to yield fragments with even proton numbers, which is called the odd-even effect on the fragments' charge distribution. However, no odd-even effect is observed on fragment mass number distribution. This result is attributed to nucleon pair breaking.

In nuclear fission events the nuclei may break into any combination of lighter nuclei, but the most common event is not fission to equal mass nuclei of about mass 120; the most common event (depending on isotope and process) is a slightly unequal fission in which one daughter nucleus has a mass of about 90 to 100 u and the other the remaining 130 to 140 u.[20]

Stable nuclei, and unstable nuclei with very long Half-lifes, follow a trend of stability evident when Z is plotted against N. For lighters nuclei less than N pf 20, the line has the slope n=Z, while the heavier nuclei require additional neutrons to remain stable. Nuclei that are neutron or proton rich have excessive binding energy for stability, and the excess energy may convert a neutron to a proton or a neutron to a proton via the weak nuclear force.[9]

Neutron-induced fission of U-235 emits total energy of 207 MeV, of which about 200 MeV is recoverable, Prompt fission fragments amount to 168 MeV, which are easily stopped with a fraction of a millimeter. Prompt neutrons total 5 MeV, and this energy is recovered as heat via scattering in the reactor. However, many fission fragments are neutron rich and decay via β^- emissions. According to Lilley, "The radioactive decay energy from the fission chains is the second release of energy due to fission. It is much less than the prompt energy, but it is a significant amount and is why reactors must continue to be cooled after they have been shut down and why the waste products must be handled with great care and stored safely."[9]

A schematic nuclear fission chain reaction. 1. A uranium-235 atom absorbs a neutron and fissions into two new atoms (fission fragments), releasing three new neutrons and some binding energy. 2. One of those neutrons is absorbed by an atom of uranium-238 and does not continue the reaction. Another neutron is simply lost and does not collide with anything, also not continuing the reaction. However, the one neutron does collide with an atom of uranium-235, which then fissions and releases two neutrons and some binding energy. 3. Both of those neutrons collide with uranium-235 atoms, each of which fissions and releases between one and three neutrons, which can then continue the reaction.

Several heavy elements, such as uranium, thorium, and plutonium, undergo both spontaneous fission, a form of radioactive decay and induced fission, a form of nuclear reaction. Elemental isotopes that undergo induced fission when struck by a free neutron are called fissionable; isotopes that undergo fission when struck by a slow-moving thermal neutron are also called fissile. A few particularly fissile and readily obtainable isotopes (notably ²³³U, ²³⁵U and ²³⁹Pu) are called nuclear fuels because they can sustain a chain reaction and can be obtained in large enough quantities to be useful.

All fissionable and fissile isotopes undergo a small amount of spontaneous fission which releases a few free neutrons into any sample of nuclear fuel. Such neutrons would escape rapidly from the fuel and become a free neutron, with a mean lifetime of about 15 minutes before decaying to protons and beta particles. However, neutrons almost invariably impact and are absorbed by other nuclei in the vicinity long before this happens (newly created fission neutrons move at about 7% of the speed of light, and even moderated neutrons move at about 8 times the speed of sound). Some neutrons will impact fuel nuclei and induce further fissions, releasing yet more neutrons. If enough nuclear fuel is assembled in one place, or if the escaping neutrons are sufficiently contained, then these freshly emitted neutrons outnumber the neutrons that escape from the assembly, and a sustained nuclear chain reaction will take place.

An assembly that supports a sustained nuclear chain reaction is called a critical assembly or, if the assembly is almost entirely made of a nuclear fuel, a critical mass. The word "critical" refers to a cusp in the behavior of the differential equation that governs the number of free neutrons present in the fuel: if less than a critical mass is present, then the amount of neutrons is determined by radioactive decay, but if a critical mass or more is present, then the amount of neutrons is controlled instead by the physics of the chain reaction. The actual mass of a critical mass of nuclear fuel depends strongly on the geometry and surrounding materials.

Not all fissionable isotopes can sustain a chain reaction. For example, ²³⁸U, the most abundant form of uranium, is fissionable but not fissile: it undergoes induced fission when impacted by an energetic neutron with over 1 MeV of kinetic energy. However, too few of the neutrons produced by ²³⁸U fission are energetic enough to induce further fissions in ²³⁸U, so no chain reaction is possible with this isotope. Instead, bombarding ²³⁸U with slow neutrons causes it to absorb them (becoming ²³⁹U) and decay by beta emission to ²³⁹Np which then decays again by the same process to ²³⁹Pu; that process is used to manufacture ²³⁹Pu in breeder reactors. In-situ plutonium production also contributes to the neutron chain reaction in other types of reactors after sufficient plutonium-239 has been produced, since plutonium-239 is also a fissile element which serves as fuel. It is estimated that up to half of the power produced by a standard "non-breeder" reactor is produced by the fission of plutonium-239 produced in place, over the total life-cycle of a fuel load.

Fissionable, non-fissile isotopes can be used as fission energy source even without a chain reaction. Bombarding ²³⁸U with fast neutrons induces fissions, releasing energy as long as the external neutron source is present. This is an important effect in all reactors where fast neutrons from the fissile isotope can cause the fission of nearby ²³⁸U nuclei, which means that some small part of the ²³⁸U is "burned-up" in all nuclear fuels, especially in fast breeder reactors that operate with higher-energy neutrons. That same fast-fission effect is used to augment the energy released by modern thermonuclear weapons, by jacketing the weapon with ²³⁸U to react with neutrons released by nuclear fusion at the center of the device. But the explosive effects of nuclear fission chain reactions can be reduced by using substances like moderators which slow down the speed of secondary neutrons.

The cooling towers of the Philippsburg Nuclear Power Plant, in Germany.

Critical fission reactors are the most common type of nuclear reactor. In a critical fission reactor, neutrons produced by fission of fuel atoms are used to induce yet more fissions, to sustain a controllable amount of energy release. Devices that produce engineered but non-self-sustaining fission reactions are subcritical fission reactors. Such devices use radioactive decay or particle accelerators to trigger fissions.

Critical fission reactors are built for three primary purposes, which typically involve different engineering trade-offs to take advantage of either the heat or the neutrons produced by the fission chain reaction:

• power reactors are intended to produce heat for nuclear power, either as part of a generating station or a local power system such as a nuclear submarine.
• research reactors are intended to produce neutrons and/or activate radioactive sources for scientific, medical, engineering, or other research purposes.
• breeder reactors are intended to produce nuclear fuels in bulk from more abundant isotopes. The better known fast breeder reactor makes ²³⁹Pu (a nuclear fuel) from the naturally very abundant ²³⁸U (not a nuclear fuel). Thermal breeder reactors previously tested using ²³²Th to breed the fissile isotope ²³³U (thorium fuel cycle) continue to be studied and developed.

While, in principle, all fission reactors can act in all three capacities, in practice the tasks lead to conflicting engineering goals and most reactors have been built with only one of the above tasks in mind. (There are several early counter-examples, such as the Hanford N reactor, now decommissioned). Power reactors generally convert the kinetic energy of fission products into heat, which is used to heat a working fluid and drive a heat engine that generates mechanical or electrical power. The working fluid is usually water with a steam turbine, but some designs use other materials such as gaseous helium. Research reactors produce neutrons that are used in various ways, with the heat of fission being treated as an unavoidable waste product. Breeder reactors are a specialized form of research reactor, with the caveat that the sample being irradiated is usually the fuel itself, a mixture of ²³⁸U and ²³⁵U. For a more detailed description of the physics and operating principles of critical fission reactors, see nuclear reactor physics. For a description of their social, political, and environmental aspects, see nuclear power.

The mushroom cloud of the atomic bomb dropped on Nagasaki, Japan, on 9 August 1945 rose over 18 kilometres (11 mi) above the bomb's hypocenter. An estimated 39,000 people were killed by the atomic bomb,[21] of whom 23,145–28,113 were Japanese factory workers, 2,000 were Korean slave laborers, and 150 were Japanese combatants.[22][23][24]

One class of nuclear weapon, a fission bomb (not to be confused with the fusion bomb), otherwise known as an atomic bomb or atom bomb, is a fission reactor designed to liberate as much energy as possible as rapidly as possible, before the released energy causes the reactor to explode (and the chain reaction to stop). Development of nuclear weapons was the motivation behind early research into nuclear fission which the Manhattan Project during World War II (September 1, 1939 – September 2, 1945) carried out most of the early scientific work on fission chain reactions, culminating in the three events involving fission bombs that occurred during the war. The first fission bomb, codenamed "The Gadget", was detonated during the Trinity Test in the desert of New Mexico on July 16, 1945. Two other fission bombs, codenamed "Little Boy" and "Fat Man", were used in combat against the Japanese cities of Hiroshima and Nagasaki on August 6 and 9 (respectively) of 1945.

Even the first fission bombs were thousands of times more explosive than a comparable mass of chemical explosive. For example, Little Boy weighed a total of about four tons (of which 60 kg was nuclear fuel) and was 11 feet (3.4 m) long; it also yielded an explosion equivalent to about 15 kilotons of TNT, destroying a large part of the city of Hiroshima. Modern nuclear weapons (which include a thermonuclear fusion as well as one or more fission stages) are hundreds of times more energetic for their weight than the first pure fission atomic bombs (see nuclear weapon yield), so that a modern single missile warhead bomb weighing less than 1/8 as much as Little Boy (see for example W88) has a yield of 475 kilotons of TNT, and could bring destruction to about 10 times the city area.

While the fundamental physics of the fission chain reaction in a nuclear weapon is similar to the physics of a controlled nuclear reactor, the two types of device must be engineered quite differently (see nuclear reactor physics). A nuclear bomb is designed to release all its energy at once, while a reactor is designed to generate a steady supply of useful power. While overheating of a reactor can lead to, and has led to, meltdown and steam explosions, the much lower uranium enrichment makes it impossible for a nuclear reactor to explode with the same destructive power as a nuclear weapon. It is also difficult to extract useful power from a nuclear bomb, although at least one rocket propulsion system, Project Orion, was intended to work by exploding fission bombs behind a massively padded and shielded spacecraft.

The strategic importance of nuclear weapons is a major reason why the technology of nuclear fission is politically sensitive. Viable fission bomb designs are, arguably, within the capabilities of many, being relatively simple from an engineering viewpoint. However, the difficulty of obtaining fissile nuclear material to realize the designs is the key to the relative unavailability of nuclear weapons to all but modern industrialized governments with special programs to produce fissile materials (see uranium enrichment and nuclear fuel cycle).

Otto Hahn and Lise Meitner in 1912

The discovery of nuclear fission occurred in 1938 in the buildings of the Kaiser Wilhelm Society for Chemistry, today part of the Free University of Berlin, following over four decades of work on the science of radioactivity and the elaboration of new nuclear physics that described the components of atoms. In 1911, Ernest Rutherford proposed a model of the atom in which a very small, dense and positively charged nucleus of protons was surrounded by orbiting, negatively charged electrons (the Rutherford model).[25] Niels Bohr improved upon this in 1913 by reconciling the quantum behavior of electrons (the Bohr model). In 1928, George Gamow proposed the Liquid drop model, which became essential to understanding the physics of fission.[5]^{: 49–51, 70–77, 228}[4]^: 6–7

In 1896, Henri Becquerel had found, and Marie Curie named, radioactivity. In 1900, Rutherford and Frederick Soddy, investigating the radioactive gas emanating from thorium, "conveyed the tremendous and inevitable conclusion that the element thorium was slowly and spontaneously transmuting itself into argon gas!"[5]^: 41–43

In 1919, following up on an earlier anomaly Ernest Marsden noted in 1915, Rutherford attempted to "break up the atom." Rutherford was able to accomplish the first artificial transmutation of nitrogen into oxygen, using alpha particles directed at nitrogen ¹⁴N + α → ¹⁷O + p.  Rutherford stated, "...we must conclude that the nitrogen atom is disintegrated," while the newspapers stated he had split the atom. This was the first observation of a nuclear reaction, that is, a reaction in which particles from one decay are used to transform another atomic nucleus. It also offered a new way to study the nucleus. Rutherford and James Chadwick then used alpha particles to "disintegrate" boron, fluorine, sodium, aluminum, and phosphorus before reaching a limitation associated with the energy of his alpha particle source.[5] Eventually, in 1932, a fully artificial nuclear reaction and nuclear transmutation was achieved by Rutherford's colleagues Ernest Walton and John Cockcroft, who used artificially accelerated protons against lithium-7, to split this nucleus into two alpha particles. The feat was popularly known as "splitting the atom", and would win them the 1951 Nobel Prize in Physics for "Transmutation of atomic nuclei by artificially accelerated atomic particles", although it was not the nuclear fission reaction later discovered in heavy elements.[26]

English physicist James Chadwick discovered the neutron in 1932.[27] Chadwick used an ionization chamber to observe protons knocked out of several elements by beryllium radiation, following up on earlier observations made by Joliot-Curies. In Chadwick's words, "...In order to explain the great penetrating power of the radiation we must further assume that the particle has no net charge..." The existence of the neutron was first postulated by Rutherford in 1920, and in the words of Chadwick, "...how on earth were you going to build up a big nucleus with a large positive charge? And the answer was a neutral particle."[5]^{: 153–165} Subsequently he communicated his findings in more detail.[28]

In the words of Richard Rhodes, referring to the neutron, "It would therefore serve as a new nuclear probe of surpassing power of penetration." Philip Morrison stated, "A beam of thermal neutrons moving at about the speed of sound...produces nuclear reactions in many materials much more easily than a beam of protons...traveling thousands of times faster." According to Rhodes, "Slowing down a neutron gave it more time in the vicinity of the nucleus, and that gave it more time to be captured." Fermi's team, studying radiative capture which is the emission of gamma radiation after the nucleus captures a neutron, studied sixty elements, inducing radioactivity in forty. In the process, they discovered the ability of hydrogen to slow down the neutrons.[5]^{: 165, 216–220}

Enrico Fermi and his colleagues in Rome studied the results of bombarding uranium with neutrons in 1934.[29] Fermi concluded that his experiments had created new elements with 93 and 94 protons, which the group dubbed ausonium and hesperium. However, not all were convinced by Fermi's analysis of his results, though he would win the 1938 Nobel Prize in Physics for his "demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons". The German chemist Ida Noddack notably suggested in 1934 that instead of creating a new, heavier element 93, that "it is conceivable that the nucleus breaks up into several large fragments."[30] However, the quoted objection comes some distance down, and was but one of several gaps she noted in Fermi's claim. Although Noddack was a renowned analytical chemist, she lacked the background in physics to appreciate the enormity of what she was proposing.[31]

The nuclear fission display at the Deutsches Museum in Munich. The table and instruments are originals,[32][33] but would not have been together in the same room.

After the Fermi publication, Otto Hahn, Lise Meitner, and Fritz Strassmann began performing similar experiments in Berlin. Meitner, an Austrian Jew, lost her Austrian citizenship with the Anschluss, the union of Austria with Germany in March 1938, but she fled in July 1938 to Sweden and started a correspondence by mail with Hahn in Berlin. By coincidence, her nephew Otto Robert Frisch, also a refugee, was also in Sweden when Meitner received a letter from Hahn dated 19 December describing his chemical proof that some of the product of the bombardment of uranium with neutrons was barium. Hahn suggested a bursting of the nucleus, but he was unsure of what the physical basis for the results were. Barium had an atomic mass 40% less than uranium, and no previously known methods of radioactive decay could account for such a large difference in the mass of the nucleus. Frisch was skeptical, but Meitner trusted Hahn's ability as a chemist. Marie Curie had been separating barium from radium for many years, and the techniques were well-known. Meitner and Frisch then correctly interpreted Hahn's results to mean that the nucleus of uranium had split roughly in half. Frisch suggested the process be named "nuclear fission", by analogy to the process of living cell division into two cells, which was then called binary fission. Just as the term nuclear "chain reaction" would later be borrowed from chemistry, so the term "fission" was borrowed from biology.[34]

News spread quickly of the new discovery, which was correctly seen as an entirely novel physical effect with great scientific—and potentially practical—possibilities. Meitner's and Frisch's interpretation of the discovery of Hahn and Strassmann crossed the Atlantic Ocean with Niels Bohr, who was to lecture at Princeton University. I.I. Rabi and Willis Lamb, two Columbia University physicists working at Princeton, heard the news and carried it back to Columbia. Rabi said he told Enrico Fermi; Fermi gave credit to Lamb. Bohr soon thereafter went from Princeton to Columbia to see Fermi. Not finding Fermi in his office, Bohr went down to the cyclotron area and found Herbert L. Anderson. Bohr grabbed him by the shoulder and said: "Young man, let me explain to you about something new and exciting in physics."[35]

It was clear to a number of scientists at Columbia that they should try to detect the energy released in the nuclear fission of uranium from neutron bombardment. On 25 January 1939, a Columbia University team conducted the first nuclear fission experiment in the United States,[36] which was done in the basement of Pupin Hall. The experiment involved placing uranium oxide inside of an ionization chamber and irradiating it with neutrons, and measuring the energy thus released. The results confirmed that fission was occurring and hinted strongly that it was the isotope uranium 235 in particular that was fissioning. The next day, the Fifth Washington Conference on Theoretical Physics began in Washington, D.C. under the joint auspices of the George Washington University and the Carnegie Institution of Washington. There, the news on nuclear fission was spread even further, which fostered many more experimental demonstrations.[37] The 6 January 1939 Hahn and Strassman paper announced the discover of fission. In their second publication on nuclear fission in February of 1939, Hahn and Strassmann used the term Uranspaltung (uranium fission) for the first time, and predicted the existence and liberation of additional neutrons during the fission process, opening up the possibility of a nuclear chain reaction.[38] The 11 February 1939 paper by Meitner and Frisch compared the process to the division of a liquid drop and estimated the energy released at 200 MeV.[39] The 1 September 1939 paper by Bohr and Wheel used this liquid drop model to quantify fission details, including the energy released, estimated the cross section for neutron-induced fission, and deduced ²³⁵
U was the major contributor to that cross section and slow-neutron fission.[40][5]^{: 262, 311}[4]^: 9–13

During this period the Hungarian physicist Leó Szilárd realized that the neutron-driven fission of heavy atoms could be used to create a nuclear chain reaction. Such a reaction using neutrons was an idea he had first formulated in 1933, upon reading Rutherford's disparaging remarks about generating power from neutron collisions. However, Szilárd had not been able to achieve a neutron-driven chain reaction using beryllium. Szilard stated, "...if we could find an element which is split by neutrons and which would emit two neutrons when it absorbs one neutron, such an element, if assembled in sufficiently large mass, could sustain a nuclear chain reaction." On 25 January 1939, after learning of Hahn's discovery from Eugene Wigner, Szilard noted, "...if enough neutrons are emitted...then it should be, of course, possible to sustain a chain reaction. All of the things which H. G. Wells predicted appeared suddenly real to me." After the Hahn-Strassman paper was published, Szilard noted in a letter to Lewis Strauss, that during the fission of uranium, "the energy released in this new reaction must be very much higher than all previously known cases...," which might lead to "large-scale production of energy and radioactive elements, unfortunately also perhaps to atomic bombs."[41][5]^{: 26–28, 203–204, 213–214, 223–225, 267–268}

Szilard now urged Fermi (in New York) and Frédéric Joliot-Curie (in Paris) to refrain from publishing on the possibility of a chain reaction, lest the Nazi government become aware of the possibilities on the eve of what would later be known as World War II. With some hesitation Fermi agreed to self-censor. But Joliot-Curie did not, and in April 1939 his team in Paris, including Hans von Halban and Lew Kowarski, reported in the journal Nature that the number of neutrons emitted with nuclear fission of uranium was then reported at 3.5 per fission.[42] Szilard and Walter Zinn found "...the number of neutrons emitted by fission to be about two." Fermi and Anderson estimated "a yield of about two neutrons per each neutron captured."[5]^{: 290–291, 295–296}

Drawing of the first artificial reactor, Chicago Pile-1.

With the news of fission neutrons from uranium fission, Szilárd immediately understood the possibility of a nuclear chain reaction using uranium. In the summer, Fermi and Szilard proposed the idea of a nuclear reactor (pile) to mediate this process. The pile would use natural uranium as fuel. Fermi had shown much earlier that neutrons were far more effectively captured by atoms if they were of low energy (so-called "slow" or "thermal" neutrons), because for quantum reasons it made the atoms look like much larger targets to the neutrons. Thus to slow down the secondary neutrons released by the fissioning uranium nuclei, Fermi and Szilard proposed a graphite "moderator", against which the fast, high-energy secondary neutrons would collide, effectively slowing them down. With enough uranium, and with sufficiently pure graphite, their "pile" could theoretically sustain a slow-neutron chain reaction. This would result in the production of heat, as well as the creation of radioactive fission products.[5]^{: 291, 298–302}

In August 1939, Szilard, Teller and Wigner thought that the Germans might make use of the fission chain reaction and were spurred to attempt to attract the attention of the United States government to the issue. Towards this, they persuaded Albert Einstein to lend his name to a letter directed to President Franklin Roosevelt. On 11 October, the Einstein–Szilárd letter was delivered via Alexander Sachs. Roosevelt quickly understood the implications, stating, "Alex, what you are after is to see that the Nazis don't blow us up." Roosevelt ordered the formation of the Advisory Committee on Uranium.[5]^{: 303–309, 312–317}

In February 1940, encouraged by Fermi and John R. Dunning, Alfred O. C. Nier was able to separate U-235 and U-238 from uranium tetrachloride in a glass mass spectrometer. Subsequently, Dunning, bombarding the U-235 sample with neutrons generated by the Columbia University cyclotron, confirmed "U-235 was responsible for the slow neutron fission of uranium."[5]^{: 297–298, 332}

At the University of Birmingham, Frisch teamed up with Peierls, who had been working on a critical mass formula. assuming isotope separation was possible, they considered ²³⁵U, which had a cross section not yet determined, but which was assumed to be much larger than that of natural uranium. They calculated only a pound or two in a volume less than a golf ball, would result in a chain reaction faster than vaporization, and the resultant explosion would generate temperature greater than the interior of the sun, and pressures greater than the center of the earth. Additionally, the costs of isotope separation "would be insignificant compared to the cost of the war." By March 1940, encouraged by Mark Oliphant, they wrote the Frisch–Peierls memorandum in two parts, "On the construction of a 'super-bomb; based on a nuclear chain reaction in uranium," and "Memorandum on the on the properties of a radioactive 'super-bomb.' ". On 10 April 1940, the first meeting of the MAUD Committee was held.[5]^{: 321–325, 330–331, 340–341}

In December 1940, Franz Simon at Oxford, wrote his Estimate of the size of an actual separation plant." In it, Simon proposed gaseous diffusion as the best method for uranium isotope separation.[5]^{: 339, 343}

On 28 March 1941, Emilio Segré and Glen Seaborg reported on the "strong indications that 94²³⁹ undergoes fission with slow neutrons." This meant chemical separation was an alternative to uranium isotope separation. Instead, a nuclear reactor fueled with ordinary uranium could produce a plutonium isotope as a nuclear explosive substitute for ²³⁵U. In May, they demonstrated the cross section of plutonium was 1.7 times that of U235. When plutonium's cross section for fast fission was measured to be ten times that of U238, plutonium became a viable option for a bomb.[5]^{: 346–355, 366–368}

In October 1941, MAUD released its final report to the U.S. Government. The report stated, "We have now reached the conclusion that it will be possible to make an effective uranium bomb...The material for the first bomb could be ready by the end of 1943..."[5]^{: 368–369}

In November 1941, John Dunning and Eugene T. Booth were able to demonstrate the enrichment of uranium through gaseous barrier diffusion. On 27 November, Bush delivered to third National Academy of Sciences report to Roosevelt. The report, amongst other things, called for parallel development of all isotope-separation systems. On 6 December, Bush and Conant reorganized the Uranium Committee's tasks, with Harold Urey developing gaseous diffusion, Lawrence developing electromagnetic separation, Eger V. Murphree developing centrifuges, and Arthur Compton responsible for theoretical studies and design.[5]^{: 381, 387–388}

On 23 April 1942, Met Lab scientists discussed seven possible ways to extract plutonium from irradiated uranium, and decided to pursue investigation of all seven. On 17 June, the first batch of uranium nitrate hexahydrate (UNH) was undergoing neutron bombardment in the Washington University in St. Louis cyclotron. On 27 July, the irradiated UNH was ready for Glenn T. Seaborg's team. On 20 August, using ultramicrochemistry techniques, they successfully extracted plutonium.[5]^{: 408–415}

In April 1939, creating a chain reaction in natural uranium became the goal of Fermi and Szilard, as opposed to isotope separation. Their first efforts involved five hundred pounds of uranium oxide from the Eldorado Radium Corporation. Packed into fifty-two cans two inches in diameter and two feet long in a tank of manganese solution, they were able to confirm more neutrons were emitted than absorbed. However, the hydrogen within the water absorbed the slow neutrons necessary for fission. Carbon in the form of graphite, was then considered, because of its smaller capture cross section. In April 1940, Fermi was able to confirm carbon's potential for a slow-neutron chain reaction, after receiving National Carbon Company's graphite bricks at their Pupin Laboratories. In August and September, the Columbia team enlarged upon the cross section measurements by making a series of exponential "piles". The first piles consisted of a uranium-graphite lattice, consisting of 288 cans, each containing 60 pounds of uranium oxide, surrounded by graphite bricks. Fermi's goal was to determine critical mass necessary to sustain neutron generation. Fermi defined the reproduction factor k for assessing the chain reaction, with a value of 1.0 denoting a sustained chain reaction. In September 1941, Fermi's team was only able to achieve a k value of 0.87. In April 1942, before the project was centralized in Chicago, they had achieved 0.918 by removing moisture from the oxide. In May 1942, Fermi planned a full-scale chain reacting pile, Chicago Pile-1, after one of the exponential piles at Stagg Field reached a k of 0.995. Between 15 September and 15 November, Herbert L. Anderson and Walter Zinn built sixteen exponential piles. Acquisition of purer forms of graphite, without traces of boron and its large cross section, became paramount. Also important was the acquisition of highly purified forms of oxide from Mallinckrodt Chemical Works. Finally, acquiring pure uranium metal from the Ames process, meant the replacement of oxide pseudospheres with Frank Spedding's "eggs". Starting on 16 November 1942, Fermi had Anderson and Zinn working in two twelve-hours shifts, constructing a pile that eventually reached 57 layers by 1 Dec. The final pile consisted of 771,000 pounds of graphite, 80,590 pounds of uranium oxide, and 12,400 pounds of uranium metal, with ten cadmium control rods. Neutron intensity was measured with a boron trifluoride counter, with the control rods removed, after the end of each shift. On 2 Dec. 1942, with k approaching 1.0, Fermi had all but one of the control rod removed, and gradually removed the last one. The neutron counter clicks increased, as did the pen recorder, when Fermi announced "The pile has gone critical." They had achieved a k of 1.0006, which meant neutron intensity doubled every two minutes, in addition to breeding plutonium.[5]^{: 298–301, 333–334, 394–397, 400–401, 428–442}

In the United States, an all-out effort for making atomic weapons was begun in late 1942. This work was taken over by the U.S. Army Corps of Engineers in 1943, and known as the Manhattan Engineer District. The top-secret Manhattan Project, as it was colloquially known, was led by General Leslie R. Groves. Among the project's dozens of sites were: Hanford Site in Washington, which had the first industrial-scale nuclear reactors and produced plutonium; Oak Ridge, Tennessee, which was primarily concerned with uranium enrichment; and Los Alamos, in New Mexico, which was the scientific hub for research on bomb development and design. Other sites, notably the Berkeley Radiation Laboratory and the Metallurgical Laboratory at the University of Chicago, played important contributing roles. Overall scientific direction of the project was managed by the physicist J. Robert Oppenheimer.

In July 1945, the first atomic explosive device, dubbed "The Gadget", was detonated in the New Mexico desert in the Trinity test. It was fueled by plutonium created at Hanford. In August 1945, two more atomic devices – "Little Boy", a uranium-235 bomb, and "Fat Man", a plutonium bomb – were used against the Japanese cities of Hiroshima and Nagasaki.

In the years after World War II, many countries were involved in the further development of nuclear fission for the purposes of nuclear reactors and nuclear weapons. The UK opened the first commercial nuclear power plant in 1956. By 2013, there were 437 reactors in 31 countries.

Criticality in nature is uncommon. At three ore deposits at Oklo in Gabon, sixteen sites (the so-called Oklo Fossil Reactors) have been discovered at which self-sustaining nuclear fission took place approximately 2 billion years ago. Unknown until 1972 (but postulated by Paul Kuroda in 1956[43]), when French physicist Francis Perrin discovered the Oklo Fossil Reactors, it was realized that nature had beaten humans to the punch. Large-scale natural uranium fission chain reactions, moderated by normal water, had occurred far in the past and would not be possible now. This ancient process was able to use normal water as a moderator only because 2 billion years before the present, natural uranium was richer in the shorter-lived fissile isotope ²³⁵U (about 3%), than natural uranium available today (which is only 0.7%, and must be enriched to 3% to be usable in light-water reactors).