Nuclear reaction

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In this symbolic representing of a nuclear reaction, lithium-6 (
) and deuterium (
) react to form the highly excited intermediate nucleus
which then decays immediately into two alpha particles of helium-4 (
). Protons are symbolically represented by red spheres, and neutrons by blue spheres. Li6-D Reaction.svg
In this symbolic representing of a nuclear reaction, lithium-6 (
) and deuterium (
) react to form the highly excited intermediate nucleus
which then decays immediately into two alpha particles of helium-4 (
). Protons are symbolically represented by red spheres, and neutrons by blue spheres.

In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle (such as a proton, neutron, or high energy electron) from outside the atom, collide to produce one or more nuclides that are different from the nuclide(s) that began the process (parent nuclei). Thus, a nuclear reaction must cause a transformation of at least one nuclide to another. If a nucleus interacts with another nucleus or particle and they then separate without changing the nature of any nuclide, the process is simply referred to as a type of nuclear scattering, rather than a nuclear reaction.

Nuclear physics field of physics that deals with the structure and behavior of atomic nuclei

Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. Other forms of nuclear matter are also studied. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons.

Nuclear chemistry branch of chemistry concerned with radioactivity, transmutation and other nuclear processes

Nuclear chemistry is the subfield of chemistry dealing with radioactivity, nuclear processes, and transformations in the nuclei of atoms, such as nuclear transmutation and nuclear properties.

Atomic nucleus core of the atom; composed of bound nucleons (protons and neutrons)

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively-charged nucleus, with a cloud of negatively-charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force.


In principle, a reaction can involve more than two particles colliding, but because the probability of three or more nuclei to meet at the same time at the same place is much less than for two nuclei, such an event is exceptionally rare (see triple alpha process for an example very close to a three-body nuclear reaction). "Nuclear reaction" is a term implying an induced changing in a nuclide, and thus it does not apply to any type of radioactive decay (which by definition is a spontaneous process).[ citation needed ]

Particle small localized object in physical sciences

In the physical sciences, a particle is a small localized object to which can be ascribed several physical or chemical properties such as volume, density or mass. They vary greatly in size or quantity, from subatomic particles like the electron, to microscopic particles like atoms and molecules, to macroscopic particles like powders and other granular materials. Particles can also be used to create scientific models of even larger objects depending on their density, such as humans moving in a crowd or celestial bodies in motion.

A collision is the event in which two or more bodies exert forces on each other in about a relatively short time. Although the most common use of the word collision refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the force.

Radioactive decay Process by which an unstable atom emits radiation

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, such as an alpha particle, beta particle with neutrino or only a neutrino in the case of electron capture, or a gamma ray or electron in the case of internal conversion. A material containing unstable nuclei is considered radioactive. Certain highly excited short-lived nuclear states can decay through neutron emission, or more rarely, proton emission.

Natural nuclear reactions occur in the interaction between cosmic rays and matter, and nuclear reactions can be employed artificially to obtain nuclear energy, at an adjustable rate, on demand. Perhaps the most notable nuclear reactions are the nuclear chain reactions in fissionable materials that produce induced nuclear fission, and the various nuclear fusion reactions of light elements that power the energy production of the Sun and stars.

Cosmic ray High-energy particle, mainly originating outside the Solar system

Cosmic rays are a form of high-energy radiation, mainly originating outside the Solar System and even from distant galaxies. Upon impact with the Earth's atmosphere, cosmic rays can produce showers of secondary particles that sometimes reach the surface. Composed primarily of high-energy protons and atomic nuclei, they are originated either from the sun or from outside of our solar system. Data from the Fermi Space Telescope (2013) have been interpreted as evidence that a significant fraction of primary cosmic rays originate from the supernova explosions of stars. Active galactic nuclei also appear to produce cosmic rays, based on observations of neutrinos and gamma rays from blazar TXS 0506+056 in 2018.

Nuclear chain reaction one single nuclear reaction causes more subsequent nuclear reactions

A nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, this leading to the possibility of a self-propagating series of these reactions. The specific nuclear reaction may be the fission of heavy isotopes. The nuclear chain reaction releases several million times more energy per reaction than any chemical reaction.

Nuclear fission nuclear reaction or a radioactive decay process is also known as nuclear fission.

In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction or a radioactive decay process in which the nucleus of an atom splits into 2 smaller, lighter nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay.


In 1919, Ernest Rutherford was able to accomplish transmutation of nitrogen into oxygen at the University of Manchester, using alpha particles directed at nitrogen 14N + α → 17O + p.  This was the first observation of an induced nuclear reaction, that is, a reaction in which particles from one decay are used to transform another atomic nucleus. Eventually, in 1932 at Cambridge University, a fully artificial nuclear reaction and nuclear transmutation was achieved by Rutherford's colleagues John Cockcroft and Ernest Walton, who used artificially accelerated protons against lithium-7, to split the nucleus into two alpha particles. The feat was popularly known as "splitting the atom", although it was not the modern nuclear fission reaction later discovered in heavy elements, in 1938 by the German scientists Otto Hahn and Fritz Strassmann. [1]

Ernest Rutherford New Zealand-born British chemist and physicist

Ernest Rutherford, 1st Baron Rutherford of Nelson,, HFRSE, LLD, was a New Zealand-born British physicist who came to be known as the father of nuclear physics. Encyclopædia Britannica considers him to be the greatest experimentalist since Michael Faraday (1791–1867).

John Cockcroft British physicist

Sir John Douglas Cockcroft, was a British physicist who shared with Ernest Walton the Nobel Prize in Physics in 1951 for splitting the atomic nucleus, and was instrumental in the development of nuclear power.

Ernest Walton Irish physicist and Nobel laureate

Ernest Thomas Sinton Walton was an Irish physicist and Nobel laureate for his work with John Cockcroft with "atom-smashing" experiments done at Cambridge University in the early 1930s, and so became the first person in history to split the atom.


Nuclear reactions may be shown in a form similar to chemical equations, for which invariant mass must balance for each side of the equation, and in which transformations of particles must follow certain conservation laws, such as conservation of charge and baryon number (total atomic mass number). An example of this notation follows:

Invariant mass bodys intrinsic mass (or equivalent intrinsic energy), motion-independent (Lorentz invariant); equals total mass (or energy) when at rest

The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system's total energy and momentum that is the same in all frames of reference related by Lorentz transformations. If a center-of-momentum frame exists for the system, then the invariant mass of a system is equal to its total mass in that "rest frame". In other reference frames, where the system's momentum is nonzero, the total mass of the system is greater than the invariant mass, but the invariant mass remains unchanged.

Mass number total number of heavy particles (protons and neutrons jointly called nucleons) in the atomic nucleus

The mass number, also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. It is approximately equal to the atomic mass of the atom expressed in atomic mass units. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion. The mass number is different for each different isotope of a chemical element. Hence, the difference between the mass number and the atomic number Z gives the number of neutrons (N) in a given nucleus: .

+  2
+ ?.

To balance the equation above for mass, charge and mass number, the second nucleus to the right must have atomic number 2 and mass number 4; it is therefore also helium-4. The complete equation therefore reads:

+  2
+  4

or more simply:

+  2
 2  4

Instead of using the full equations in the style above, in many situations a compact notation is used to describe nuclear reactions. This style of the form A(b,c)D is equivalent to A + b producing c + D. Common light particles are often abbreviated in this shorthand, typically p for proton, n for neutron, d for deuteron, α representing an alpha particle or helium-4, β for beta particle or electron, γ for gamma photon, etc. The reaction above would be written as Li-6(d,α)α. [2] [3]

Alpha particle helium-4 nucleus; a particles consisting of two protons and two neutrons bound together

Alpha particles, also called alpha ray or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produced in other ways. Alpha particles are named after the first letter in the Greek alphabet, α. The symbol for the alpha particle is α or α2+. Because they are identical to helium nuclei, they are also sometimes written as He2+
or 4
indicating a helium ion with a +2 charge. If the ion gains electrons from its environment, the alpha particle becomes a normal helium atom 4

Helium-4 isotope of helium

Helium-4 is a non-radioactive isotope of the element helium. It is by far the most abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consists of two protons and two neutrons.

Beta particle ionizing radiation

A beta particle, also called beta ray or beta radiation, is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during the process of beta decay. There are two forms of beta decay, β decay and β+ decay, which produce electrons and positrons respectively.

Energy conservation

Kinetic energy may be released during the course of a reaction (exothermic reaction) or kinetic energy may have to be supplied for the reaction to take place (endothermic reaction). This can be calculated by reference to a table of very accurate particle rest masses, [4] as follows: according to the reference tables, the 6
nucleus has a standard atomic weight of 6.015 atomic mass units (abbreviated u), the deuterium has 2.014 u, and the helium-4 nucleus has 4.0026 u. Thus:

In a nuclear reaction, the total (relativistic) energy is conserved. The "missing" rest mass must therefore reappear as kinetic energy released in the reaction; its source is the nuclear binding energy. Using Einstein's mass-energy equivalence formula E = mc², the amount of energy released can be determined. We first need the energy equivalent of one atomic mass unit:

1 u  = (1.66054 × 10−27 kg) × (2.99792 × 108 m/s)² 
= 1.49242 × 10−10 kg (m/s)² = 1.49242 × 10−10 J (joule) × (1  MeV  / 1.60218 × 10−13 J)
= 931.49 MeV,
so 1 u  = 931.49 MeV.

Hence, the energy released is 0.0238 × 931 MeV = 22.2 MeV.

Expressed differently: the mass is reduced by 0.3%, corresponding to 0.3% of 90 PJ/kg is 270 TJ/kg.

This is a large amount of energy for a nuclear reaction; the amount is so high because the binding energy per nucleon of the helium-4 nucleus is unusually high, because the He-4 nucleus is "doubly magic". (The He-4 nucleus is unusually stable and tightly bound for the same reason that the helium atom is inert: each pair of protons and neutrons in He-4 occupies a filled 1s nuclear orbital in the same way that the pair of electrons in the helium atom occupy a filled 1s electron orbital). Consequently, alpha particles appear frequently on the right hand side of nuclear reactions.

The energy released in a nuclear reaction can appear mainly in one of three ways:

When the product nucleus is metastable, this is indicated by placing an asterisk ("*") next to its atomic number. This energy is eventually released through nuclear decay.

A small amount of energy may also emerge in the form of X-rays. Generally, the product nucleus has a different atomic number, and thus the configuration of its electron shells is wrong. As the electrons rearrange themselves and drop to lower energy levels, internal transition X-rays (X-rays with precisely defined emission lines) may be emitted.

Q-value and energy balance

In writing down the reaction equation, in a way analogous to a chemical equation, one may in addition give the reaction energy on the right side:

Target nucleus + projectile → Final nucleus + ejectile + Q.

For the particular case discussed above, the reaction energy has already been calculated as Q = 22.2 MeV. Hence:

+  2
 2  4
+ 22.2  MeV.

The reaction energy (the "Q-value") is positive for exothermal reactions and negative for endothermal reactions, opposite to the similar expression in chemistry. On the one hand, it is the difference between the sums of kinetic energies on the final side and on the initial side. But on the other hand, it is also the difference between the nuclear rest masses on the initial side and on the final side (in this way, we have calculated the Q-value above).

Reaction rates

If the reaction equation is balanced, that does not mean that the reaction really occurs. The rate at which reactions occur depends on the particle energy, the particle flux and the reaction cross section. An example of a large repository of reaction rates is the REACLIB database, as maintained by the Joint Institute for Nuclear Astrophysics.

Neutrons vs. ions

In the initial collision which begins the reaction, the particles must approach closely enough so that the short range strong force can affect them. As most common nuclear particles are positively charged, this means they must overcome considerable electrostatic repulsion before the reaction can begin. Even if the target nucleus is part of a neutral atom, the other particle must penetrate well beyond the electron cloud and closely approach the nucleus, which is positively charged. Thus, such particles must be first accelerated to high energy, for example by:

Also, since the force of repulsion is proportional to the product of the two charges, reactions between heavy nuclei are rarer, and require higher initiating energy, than those between a heavy and light nucleus; while reactions between two light nuclei are the most common ones.

Neutrons, on the other hand, have no electric charge to cause repulsion, and are able to initiate a nuclear reaction at very low energies. In fact, at extremely low particle energies (corresponding, say, to thermal equilibrium at room temperature), the neutron's de Broglie wavelength is greatly increased, possibly greatly increasing its capture cross section, at energies close to resonances of the nuclei involved. Thus low-energy neutrons may be even more reactive than high energy neutrons.

Notable types

While the number of possible nuclear reactions is immense, there are several types which are more common, or otherwise notable. Some examples include:

Direct reactions

An intermediate energy projectile transfers energy or picks up or loses nucleons to the nucleus in a single quick (10−21 second) event. Energy and momentum transfer are relatively small. These are particularly useful in experimental nuclear physics, because the reaction mechanisms are often simple enough to calculate with sufficient accuracy to probe the structure of the target nucleus.

Inelastic scattering

Only energy and momentum are transferred.

  • (p,p') tests differences between nuclear states.
  • (α,α') measures nuclear surface shapes and sizes. Since α particles that hit the nucleus react more violently, elastic and shallow inelastic α scattering are sensitive to the shapes and sizes of the targets, like light scattered from a small black object.
  • (e,e') is useful for probing the interior structure. Since electrons interact less strongly than do protons and neutrons, they reach to the centers of the targets and their wave functions are less distorted by passing through the nucleus.

Transfer reactions

Usually at moderately low energy, one or more nucleons are transferred between the projectile and target. These are useful in studying outer shell structure of nuclei.

  • (α,n) and (α,p) reactions. Some of the earliest nuclear reactions studied involved an alpha particle produced by alpha decay, knocking a nucleon from a target nucleus.
  • (d,n) and (d,p) reactions. A deuteron beam impinges on a target; the target nuclei absorb either the neutron or proton from the deuteron. The deuteron is so loosely bound that this is almost the same as proton or neutron capture. A compound nucleus may be formed, leading to additional neutrons being emitted more slowly. (d,n) reactions are used to generate energetic neutrons.
  • The strangeness exchange reaction (K, π) has been used to study hypernuclei.
  • The reaction 14N(α,p)17O performed by Rutherford in 1917 (reported 1919), is generally regarded as the first nuclear transmutation experiment.

Reactions with neutrons

T 7Li 14C
(n,α) 6Li + n → T + α 10B + n → 7Li + α17O + n → 14C + α21Ne + n → 18O + α37Ar + n → 34S + α
(n,p) 3He + n → T + p7Be + n → 7Li + p 14N + n → 14C + p22Na + n → 22Ne + p
(n,γ) 2H + n → T + γ13C + n → 14C + γ

Reactions with neutrons are important in nuclear reactors and nuclear weapons. While the best-known neutron reactions are neutron scattering, neutron capture, and nuclear fission, for some light nuclei (especially odd-odd nuclei) the most probable reaction with a thermal neutron is a transfer reaction:

Some reactions are only possible with fast neutrons:

Compound nuclear reactions

Either a low-energy projectile is absorbed or a higher energy particle transfers energy to the nucleus, leaving it with too much energy to be fully bound together. On a time scale of about 10−19 seconds, particles, usually neutrons, are "boiled" off. That is, it remains together until enough energy happens to be concentrated in one neutron to escape the mutual attraction. The excited quasi-bound nucleus is called a compound nucleus.

See also

Related Research Articles

Alpha decay emission of alpha particles by a decaying radioactive atom

Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an atomic number that is reduced by two. An alpha particle is identical to the nucleus of a helium-4 atom, which consists of two protons and two neutrons. It has a charge of +2 e and a mass of 4 u. For example, uranium-238 decays to form thorium-234. Alpha particles have a charge +2 e, but as a nuclear equation describes a nuclear reaction without considering the electrons – a convention that does not imply that the nuclei necessarily occur in neutral atoms – the charge is not usually shown.

Beta decay decay where electrons (β-, beta minus) or positrons (β+, positron emission) are emitted

In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle is emitted from an atomic nucleus, transforming the original nuclide to its isobar. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in so-called positron emission. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form what is called the nuclear band or valley of stability. For either electron or positron emission to be energetically possible, the energy release or Q value must be positive.

Neutron nucleon (constituent of the nucleus of the atom) that has neutral electric charge (no charge); symbol n

The neutron is a subatomic particle, symbol
, with no net electric charge and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behave similarly within the nucleus, and each has a mass of approximately one atomic mass unit, they are both referred to as nucleons. Their properties and interactions are described by nuclear physics.

Particle radiation is the radiation of energy by means of fast-moving subatomic particles. Particle radiation is referred to as a particle beam if the particles are all moving in the same direction, similar to a light beam.

Proton–proton chain reaction One of the fusion reactions by which stars convert hydrogen to helium

The proton–proton chain reaction is one of two known sets of nuclear fusion reactions by which stars convert hydrogen to helium. It dominates in stars with masses less than or equal to that of the Sun, whereas the CNO cycle, the other known reaction, is suggested by theoretical models to dominate in stars with masses greater than about 1.3 times that of the Sun.

Binding energy forms of energy

In physics, binding energy is the minimum energy required to disassemble a system of particles into separate parts. This energy is equal to the mass defect minus the amount of energy, or mass, that is released when a bound system is created, and is what keeps the system together.

Ionizing radiation Radiation that carries enough light energy to liberate electrons from atoms or molecules

Ionizing radiation is radiation that carries sufficient energy to detach electrons from atoms or molecules, thereby ionizing them. Ionizing radiation is made up of energetic subatomic particles, ions or atoms moving at high speeds, and electromagnetic waves on the high-energy end of the electromagnetic spectrum.

Neutron emission decay where a neutron is ejected from the nucleus

Neutron emission is a mode of radioactive decay in which one or more neutrons are ejected from a nucleus. It occurs in the most neutron-rich/proton-deficient nucleides, and also from excited states of other nucleides as in photoneutron emission and beta-delayed neutron emission. As only a neutron is lost by this process the number of protons remains unchanged, and an atom does not become an atom of a different element, but a different isotope of the same element.

Neutron radiation ionizing radiation

Neutron radiation is a form of ionizing radiation that presents as free neutrons. Typical phenomena are nuclear fission or nuclear fusion causing the release of free neutrons, which then react with nuclei of other atoms to form new isotopes—which, in turn, may trigger further neutron radiation. Free neutrons are unstable, decaying into a proton, an electron, plus an anti-electron-neutrino with a mean lifetime of 887 seconds.

Nuclear binding energy energy required to split a nucleus of an atom into its component parts.

Nuclear binding energy is the minimum energy that would be required to disassemble the nucleus of an atom into its component parts. These component parts are neutrons and protons, which are collectively called nucleons. The binding energy is always a positive number, as we need to spend energy in moving these nucleons, attracted to each other by the strong nuclear force, away from each other. The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons, according to Einstein's equation E=mc2. This 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed.

Valley of stability Region of the Chart of the Nuclides with few radioactive isotopes

In nuclear physics, the valley of stability is a characterization of the stability of nuclides to radioactivity based on their binding energy. Nuclides are composed of protons and neutrons. The shape of the valley refers to the profile of binding energy as a function of the numbers of neutrons and protons, with the lowest part of the valley corresponding to the region of most stable nuclei. The line of stable nuclides down the center of the valley of stability is known as the line of beta stability. The sides of the valley correspond to increasing instability to beta decay. The decay of a nuclide becomes more energetically favorable the further it is from the line of beta stability. The boundaries of the valley correspond to the nuclear drip lines, where nuclides become so unstable they emit single protons or single neutrons. Regions of instability within the valley at high atomic number also include radioactive decay by alpha radiation or spontaneous fission. The shape of the valley is roughly an elongated paraboloid corresponding to the nuclide binding energies as a function of neutron and atomic numbers.

Ternary fission type of nuclear fission

Ternary fission is a comparatively rare type of nuclear fission in which three charged products are produced rather than two. As in other nuclear fission processes, other uncharged particles such as multiple neutrons and gamma rays are produced in ternary fission.

Discovery of the neutron

The discovery of the neutron and its properties was central to the extraordinary developments in atomic physics in the first half of the 20th century. Early in the century, Ernest Rutherford developed a crude model of the atom, based on the gold foil experiment of Hans Geiger and Ernest Marsden. In this model, atoms had their mass and positive electric charge concentrated in a very small nucleus. By 1920 chemical isotopes had been discovered, the atomic masses had been determined to be (approximately) integer multiples of the mass of the hydrogen atom, and the atomic number had been identified as the charge on the nucleus. Throughout the 1920s, the nucleus was viewed as composed of combinations of protons and electrons, the two elementary particles known at the time, but that model presented several experimental and theoretical contradictions.


  1. Cockcroft and Walton split lithium with high energy protons April 1932. Archived 2012-09-02 at the Wayback Machine
  2. The Astrophysics Spectator: Hydrogen Fusion Rates in Stars
  3. Tilley, R. J. D. (2004). Understanding Solids: The Science of Materials. John Wiley and Sons. p. 495. ISBN   0-470-85275-5.
  4. Suplee, Curt (23 August 2009). "Atomic Weights and Isotopic Compositions with Relative Atomic Masses". NIST.
  5. Shinn, E.; Et., al. (2013). "Nuclear energy conversion with stacks of graphene nanocapacitors". Complexity. Bibcode:2013Cmplx..18c..24S. doi:10.1002/cplx.21427.