Nuclear Fission

Also known as atomic fission—is a process in nuclear physics and nuclear chemistry in which the nucleus of an atom splits into two or more smaller nuclei as fission products, and usually some by-product particles. Hence, fission is a form of elemental transmutation.  The by-products include free neutrons, photons usually in the form gamma rays, and other nuclear fragments such as beta particles and alpha particles.  Fission of heavy elements is an exothermic reaction and can release substantial amounts of useful energy both as gamma rays and as kinetic energy of the fragments (heating the bulk material where fission takes place).

Nuclear fission produces energy for nuclear power and to drive explosion of nuclear weapons.  Fission is useful as a power source because some materials, called nuclear fuels, generate neutrons as part of the fission process and undergo triggered fission when impacted by a free neutron. Nuclear fuels can be part of a self-sustaining chain reaction that releases energy at a controlled rate in a nuclear reactor or at a very rapid uncontrolled rate in a nuclear weapon.

The amount of free energy contained in nuclear fuel is millions of times the amount of free energy contained in a similar mass of chemical fuel such as gasoline, making nuclear fission a very tempting source of energy; however, the waste products of nuclear fission are highly radioactive and remain so for millennia, giving rise to a nuclear waste problem.  Concerns over nuclear waste accumulation and over the immense destructive potential of nuclear weapons counterbalance the desirable qualities of fission as an energy source, and give rise to intense ongoing political debate over nuclear power.

Physical Overview

Nuclear fission differs from other forms of radioactive decay in that it can be harnessed and controlled via a chain reaction: free neutrons released by each fission event can trigger yet more events, which in turn release more neutrons and cause more fissions.  Chemical 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 an atomic mass of 235) and 239Pu (the isotope of plutonium with an atomic mass of 239). These fuels break apart into a range of chemical elements with atomic masses near 100 (fission products). Most nuclear fuels undergo spontaneous fission only very slowly, decaying mainly via an alpha/beta decay chain over periods of millennia to eons.  In a nuclear reactor or nuclear weapon, most fission events are induced by bombardment with another particle such as a neutron.

Typical fission events release several hundred MeV of energy for each fission event, which is why nuclear fission is used as an energy source.  By contrast, most chemical oxidation reactions (such as burning coal or TNT) release at most a few tens of eV per event, so nuclear fuel contains at least ten million times more usable energy than does chemical fuel. The energy of nuclear fission is released as kinetic energy of the fission products and fragments, and as electromagnetic radiation in the form of gamma rays; in a nuclear reactor, the energy is converted to heat as the particles and gamma rays collide with the atoms that make up the reactor and its working fluid, usually water or occasionally heavy water.

Nuclear fission of heavy elements produces energy because the specific binding energy (binding energy per mass) of intermediate-mass nuclei with atomic numbers and atomic masses close to 61Ni and 56Fe is greater than the specific binding energy of very heavy nuclei, so that energy is released when heavy nuclei are broken apart.

The total rest masses of the fission products (Mp) from a single reaction is less than the mass of the original fuel nucleus (M). The excess mass ?m = M - Mp is the invariant mass of the energy that is released as photons (gamma rays) and kinetic energy of the fission fragments, according to Einstein's relation E = mc2.

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.  Unequal fissions are energetically more favorable because this allows one product to be closer to the energetic minimum near mass 60 u (only a quarter of the average fissionable mass), while the other nucleus with mass 135 u is still not far out of the range of the most tightly bound nuclei (another statement of this, is that the atomic binding energy curve is slightly steeper to the left of mass 120 u than to the right of it).

Fission Fragments

frag1.gif (8347 bytes)

When uranium-235 undergoes fission, the average of the fragment mass is about 118, but very few fragments near that average are found. It is much more probable to break up into unequal fragments, and the most probable fragment masses are around mass 95 and 137. Most of these fission fragments are highly unstable (radioactive), and some of them such as cesium-137 and strontium-90 are extremely dangerous when released to the environment.

Fission Fragment Example

frag2.gif (8814 bytes)

A common pair of fragments from uranium-235 fission is xenon and strontium:

frag3.gif (2056 bytes)

Highly radioactive, the xenon decays with a half-life of 14 seconds and finally produces the stable isotope cerium-140. Strontium-94 decays with a half-life of 75 seconds, finally producing the stable isotope zirconium-94.  These fragments are not so dangerous as intermediate half-life fragments such as cesium-137. 

Fission Fragment Decay

This particular set of fragments from Uranium-235 fission undergoes a series of beta decays to form stable end products.

frag4.gif (12711 bytes)


Cesium-137 andstrontium-90 are the most dangerous radioisotopes to the environment in terms of their long-term effects. Their intermediate half-lives of about 30 years suggests that they are not only highly radioactive but that they have a long enough hal-flife to be around for hundreds of years.  Iodine-131 may give a higher initial dose, but its short half-life of 8 days ensures that it will soon be gone.  Besides its persistence and high activity, cesium-137 has the further insidious property of being mistaken for potassium by living organisms and taken up as part of the fluid electrolytes. This means that it is passed on up the food chain and reconcentrated from the environment by that process.


Strontium-90 and cesium-137 are the radioisotopes which should be most closely gaurded against release into the environment.  They both have intermediate halflives of around 30 years, which is the worst range for half-lives of radioactive contaminants.   It ensures that they are not only highly radioactive but also have a long enough halflife to be around for hundreds of years.  Strontium-90 mimics the properties of calcium and is taken up by living organisms and made a part of their electrolytes as well as deposited in bones.  As a part of the bones, it is not subsequently excreted like cesium-137 would be.  It has the potential for causing cancer or damaging the rapidly reproducing bone marrow cells.

Strontium-90 is not quite as likely as cesium-137 to be released as a part of a nuclear reactor accident because it is much less volatile, but is probably the most dangerous components of the radioactive fallout from a nuclear weapon.


Iodine-131 is a major concern in any kind of radiation release from a nuclear accident because it is volatile and because it is highly radioactive, having an 8 day half-life. It is of further concern in the human body because iodine is quickly swept up by the thyroid, so that the total intake of iodine becomes concentrated there. The thyroid has a maximum uptake of iodine, however, so some protection against iodine releases can be afforded by taking potassium iodide tablets to load up the thyroid to capacity so that radioactive iodine would be more likely to be excreted.

Neutron and proton counts for all stable atomic nuclei.  The slight upward bend to ther curve ensures that fission products are too heavy to be stable, giving rise to the nuclear waste problem.

The variation in specific binding energy with atomic number is due to the interplay of the two fundamental forces acting on the component nucleons (protons and neutrons) that make up the nucleus.  Nuclei are bound by an attractive strong nuclear force between nucleons, which overcomes the electrostatic repulsion between protons.  However, the strong nuclear force acts only over extremely short ranges, since it follows a Yukawa potential.  For this reason large nuclei are less tightly bound per unit mass than small nuclei, and breaking a very large nucleus into two or more intermediate-sized nuclei releases energy.

Because of the short range of the strong binding force, large nuclei must contain proportionally more neutrons than do light elements, which are most stable with a 1-1 ratio of protons and neutrons. Extra neutrons stabilize heavy elements because they add to strong-force binding without adding to proton-proton repulsion. Fission products have, on average, about the same ratio of neutrons and protons as their parent nucleus, and are therefore usually unstable because they have proportionally too many neutrons compared to stable isotopes of similar mass. This is the fundamental cause of the problem of radioactive high level waste from nuclear reactors.  Fission products tend to be beta emitters, emitting fast-moving electron to conserve electric charge as excess neutrons convert to protons inside the nucleus of the fission product atoms.

The most common nuclear fuels, 235U and 239Pu, are not major radiologic hazards by themselves: 235U has a half-life of approximately 700 million years, and although 239Pu has a half-life of only about 24,000 years, it is a pure alpha particle emitter and hence not particularly dangerous unless ingested.   Once a fuel element has been used, the remaining fuel material is intimately mixed with highly radioactive fission products that emit energetic beta particles and gamma rays.  Some fission products have half-lives as short as seconds; others have half-lives of tens of thousands of years, requiring long-term storage in facilities such as Yucca Mountain until the fission products decay into non-radioactive stable isotopes.

Spontaneous and Induced Fission: Chain Reactions

Many 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 thermal, slow moving neutron are also called fissile.  A few particularly fissile and readily obtainable isotopes (notably 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. The neutrons typically escape rapidly from the fuel and become a free neutron, with a half-life of about 15 minutes before they decay to protons and beta rays. The neutrons usually impact and are absorbed by other nuclei in the vicinity before this happens. However, some neutrons will impact fuel nuclei and induce further fissions, releasing yet more neutrons. If enough nuclear fuel is assembled into one place, or if the escaping neutrons are sufficiently contained, then these freshly generated neutrons out number 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, 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. But 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 239Pu; that process is used to manufacture 239Pu in breeder reactors, but does not contribute to a neutron chain reaction.

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. That 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.

Fission Reactors

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 radioative 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:

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.

Fission Bombs

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: the Manhattan Project of the U.S. military during World War II carried out most of the early scientific work on fission chain reactions, culminating in the Little Boy and Fat Man bombs that were exploded over Hiroshima and Nagasaki, Japan in August 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 yielded an explosion equivalent to about 15,000 tons 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 literally hundreds of times more energetic for their weight than the first pure fission atomic bombs, so that a modern single missile warhead bomb weighing less than 1/8th as much as Little Boy has a yield of 475,000 tons of TNT, and could bring destruction to 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.  It would be extremely difficult to convert a nuclear reactor to cause a true nuclear explosion (though fuel meltdowns and steam explosions have occurred), and similarly difficult to extract useful power from a nuclear explosive (though at least one rocket propulsion system, Project Orion, was intended to work by exploding fission bombs behind a massively padded vehicle).

The strategic importance of nuclear weapons is a major reason why the technology of nuclear fission is politically sensitive. Viable fission bomb designs are within the capabilities of bright undergraduates, but nuclear fuel to realize the designs is thought to be difficult to obtain.


The results of the bombardment of uranium by neutrons had proved interesting and puzzling.  First studied by Enrico Fermi and his colleagues in 1934, they were not properly interpreted until several years later.

On January 16, 1939, Niels Bohr of Copenhagen, Denmark, arrived in the United States to spend several months in Princeton, New Jersey, and was particularly anxious to discuss some abstract problems with Albert Einstein.  (Four years later Bohr was to escape to Sweden from Nazi-occupied Denmark in a small boat, along with thousands of other Danish Jews, in large scale operation.) Just before Bohr left Denmark, two of his colleagues, Otto Robert Frisch and Lise Meitner (both refugees from Germany), had told him their guess that the absorption of a neutron by a uranium nucleus sometimes caused that nucleus to split into approximately equal parts with the release of enormous quantities of energy, a process that Frisch dubbed "nuclear fission" (fission, as previously used up to this point, was a term which was borrowed from biology, where it was and is used to describe the splitting of one living cell into two). In 1939, Frisch and Meitner submitted their article "Disintegration of uranium by neutrons: a new type of nuclear reaction" to the scientific journal Nature.

The occasion for this hypothesis was the basic and historically most momentous discovery of Otto Hahn and Fritz Strassmann in Germany (published in their first famous article in Naturwissenschaften, January 6, 1939 which proved that an isotope of barium was produced by neutron bombardment of uranium.

The combination of the paper on the experimental and chemistry part of Hahn with the physics paper of Meitner were the foundation of most of the later research on nuclear fission, the claims that the Nobel Prize in Chemistry 1944 should have been given to all participating scientists have raised on several occasions. 

Bohr had promised to keep the Meitner/Frisch interpretation secret until their paper was published to preserve priority, but on the boat he discussed it with Leon Rosenfeld, but forgot to tell him to keep it secret. Rosenfeld immediately upon arrival told everyone at Princeton University, and from them the news spread by word of mouth to neighboring physicists including Enrico Fermi at Columbia University.  As a result of conversations among Fermi, John R. Dunning, and G.B. Pegram, a search was undertaken at Columbia for the heavy pulses of ionization that would be expected from the flying fragments of the uranium nucleus. On January 26, 1939, there was a conference on theoretical physics at Washington, D.C., sponsored jointly by the George Washington University and the Carnegie Institution of Washington.

Fermi left New York to attend this meeting before the Columbia fission experiments had been tried. At the meeting Bohr and Fermi discussed the problem of fission, and in particular Fermi mentioned the possibility that neutrons might be emitted during the process. Although this was only a guess, its implication of the possibility of a nuclear chain reaction was obvious.  "Chain reactions" at that time were a known phenomenon in chemistry, but the analogous process in nuclear physics using neutrons had been foreseen as early as 1933 by Leo Szilard, although Szilard at that time had no idea with what materials the process might be initiated. Now, with the discovery of neutron-induced fission of heavy elements, a number of sensational articles were published in the press on the subject of nuclear chain reactions. Before the meeting in Washington was over, several other experiments to confirm fission had been initiated, and positive experimental confirmation was reported from four laboratories (Columbia University, Carnegie Institution of Washington, Johns Hopkins University, Univeristy of California) in the February 15, 1939, issue of the Physical Review. By this time Bohr had heard that similar experiments had been made in his laboratory in Copenhagen about January 15.   (Letter by Frisch to Nature dated January 16, 1939, and appearing in the February 18 issue.)   Frederic Joliot in Paris had also published his first results in the Comptes Rendus of January 30, 1939).  From this time on there was a steady flow of papers on the subject of fission, so that by the time (December 6, 1939) L. A. Turner of Princeton wrote a review article on the subject in the Reviews of Modern Physics nearly one hundred papers had appeared. Complete analysis and discussion of these papers have appeared in Turner's article and elsewhere.

A major focus of early fission research was on producing a controllable nuclear chain reaction, which would mark the first harnessing of nuclear power. This led to the development of Chicago Pile-1, the world's first man-made critical nuclear reactor (which used uranium, the only natural nuclear fuel available in macroscopic quantities), and then to the Manhattan project to develop a nuclear weapon.

Producing a fission chain reaction in uranium fuel is far from trivial. Early nuclear reactors did not use isotopically enriched uranium, and in consequence they were required to use large quantities of highly purified graphite as neutron moderation materials. Use of ordinary water (as opposed to heavy water) in nuclear reactors requires enriched fuel--- the partial separation and relative enrichment of the rare 235U isotope from the far more common 238U isotope. Typically, reactors also require inclusion of extremely chemically pure neutron moderator materials such as deuterium (in heavy water), helium, beryllium, or carbon, usually as the graphite (The high purity is required because many chemical impurities such as the boron-10 component of natural boron, are very strong neutron absorbers and thus poison the chain reaction).

Production of such materials at industrial scale had to be solved for nuclear power generation and weapons production to be accomplished. Up to 1940, the total amount of uranium metal produced in the USA was not more than a few grams and even this was of doubtful purity; of metallic beryllium not more than a few kilograms; concentrated deuterium oxide (heavy water) not more than a few kilograms; and finally carbon had never been produced in quantity with anything like the purity required of a moderator.

The problem of producing large amounts of high purity uranium was solved by Frank Spedding using the thermite process.  Ames Laboratory was established in 1942 to produce the large amounts of natural (unenriched) uranium that would be necessary for the research to come. The success of the Chicago Pile-1 which used unenriched (natural) uranium, like all of the atomic "piles" which produced the plutonium for the atomic bomb, was also due specifically to Szilard's realization that very pure graphite could be used for the moderator of even natural uranium "piles". In wartime Germany, failure to appreciate the qualities of very pure graphite led to reactor designs dependent on heavy water, which in turn was denied the Germans by allied attacks in Norway, where heavy water was produced. These difficulties prevented the Nazis from building a nuclear reactor capable of criticality during the war.

Unknown until 1972, when French physicist Francis Perrin discovered the Oklo Fossil Reactors, nature had beaten humans to the punch by engaging in large-scale uranium fission chain reactions, some 2,000 million years in the past. This ancient process was able to use normal water as a moderator, only because 2,000 million years in the past, natural uranium was "enriched" with the shorter-lived fissile isotope 235U, as compared with the natural uranium available today.

Nuclear Fission

If a massive nucleus like uranium-235 breaks apart (fissions), then there will be a net yield of energy because the sum of the masses of the fragments will be less than the mass of the uranium nucleus. If the mass of the fragments is equal to or greater than that of iron at the peak of the binding energy curve, then the nuclear particles will be more tightly bound than they were in the uranium nucleus, and that decrease in mass comes off in the form of energy according to the Einstein equation.  For elements lighter than iron, fusion will yield energy.

The fission of U-235 in reactors is triggered by the absorption of a low energy neutron, often termed a "slow neutron" or a "thermal neutron". Other fissionable isotopes which can be induced to fission by slow neutrons are plutonium-239, uranium-233, and thorium-232.

fis1.gif (5101 bytes)

Uranium-235 Fission

In one of the most remarkable phenomena in nature, a slow neutron can be captured by a uranium-235 nucleus, rendering it unstable toward nuclear fission.  A fast neutron will not be captured, so neutrons must be slowed down by moderation to increase their capture probability in fission reactors.  A single fision event can yield over 200 million times the energy of the neutron which triggered it.

fis2.gif (9168 bytes)

Uranium Fuel

Natural uranium is composed of 0.72% U-235 (the fissionable isotope), 99.27% U-238, and a trace quantity 0.0055% U-234 . The 0.72% U-235 is not sufficient to produce a self-sustaining critical chain reaction in U.S. style light-water reactors, although it is used in Canadian (CANDU) reactors. For light-water reactors, the fuel must be enriched to 2.5-3.5% U-235.

Uranium is found as uranium oxide which when purified has a rich yellow color and is called "yellowcake". After reduction, the uranium must go through an isotope enrichment process. Even with the necessity of enrichment, it still takes only about 3 kg of natural uranium to supply the energy needs of one American for a year.

uore.gif (469 bytes)

Fissionable Isotopes

While uranium-235 is the naturally occuring fissionable isotope, there are other isotopes which can be induced to fission by neutron bombardment. Plutonium-239 is also fissionable by bombardment with slow neutrons, and both it and uranium-235 have been used to make nuclear fission bombs. Plutonium-239 can be produced by "breeding" it from uranium-238. Uranium-238, which makes up 99.3% of natural uranium, is not fissionable by slow neutrons. U-238 has a small probability for spontaneous fission and also a small probability of fission when bombarded with fast neutrons, but it is not useful as a nuclear fuel source. Some of the nuclear reactors at Hanford, Washington and the Savannah-River Plant (SC) are designed for the production of bomb-grade plutonium-239. Thorium-232 is fissionable, so could conceivably be used as a nuclear fuel. The only other isotope which is known to undergo fission upon slow-neutron bombardment is uranium-233.

History of U-235 Fission

In the 1930s, German physicists/chemists Otto Hahn and Fritz Strassman attempted to create transuranic elements by bombarding uranium with neutrons. Rather than the heavy elements they expected, they got several unidentified products. When they finally identified one of the products as Barium-141, they were reluctant to publish the finding because it was so unexpected. When they finally published the results in 1939, they came to the attention of Lise Meitner, an Austrian-born physicist who had worked with Hahn on his nuclear experiments. Upon Hitler's invasion of Austria, she had been forced to flee to Sweden where she and Otto Frisch, her nephew, continued to work on the neutron bombardment problem. She was the first to realize that Hahn's barium and other lighter products from the neutron bombardment experiments were coming from the fission of U-235. Frisch and Meitner carried out further experiments which showed that the U-235 fission yielded an enormous amount of energy, and that the fission yielded at least two neutrons per neutron absorbed in the interaction. They realized that this made possible a chain reaction with an unprecedented energy yield.

Uranium-235 Fission

u2351.gif (25901 bytes)

Uranium-235 Fission Example

u2352.gif (23623 bytes)

Energy From Uranium Fission

Form of Energy Released Amount of Energy Released (MeV)
Kinetic energy of two fission fragments


Immediate gamma rays


Delayed gamma rays


Fission neutrons


Energy of decay products of fission fragments


Gamma rays


Beta particles




Average total energy released

215 MeV

u235fission.gif (14675 bytes)

If at least one neutron from each fission strikes another U-235 nucleus and initiates fission, then the chain reaction is sustained.

Uranium-235 Chain Reaction

u235fissionsm.gif (8808 bytes)

A fission chain reaction produces intermediate mass fragments which are highly radioactive and produce further energy by their radioactive decay. Some of them produce neutrons, called delayd neutrons, which contribute to the fission chain reaction.

If an least one neutron from U-235 fission strikes another nucleus and causes it to fission, then the chain reaction will continue. If the reaction will sustain itself, it is said to be "critical", and the mass of U-235 required to produced the critical condition is said to be a "critical mass".  A critical chain reaction can be achieved at low concentrations of U-235 if the neutrons from fission are moderated to lower their speed, since the probability for fission with slow neutrons is greater.