Binding energy

Last updated March 13, 2024

In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts.^[1] In the former meaning the term is predominantly used in condensed matter physics, atomic physics, and chemistry, whereas in nuclear physics the term separation energy is used.

Types of binding energy

There are several types of binding energy, each operating over a different distance and energy scale. The smaller the size of a bound system, the higher its associated binding energy.

Type	Description	Example	Level
Gravitational binding energy	The gravitational binding energy of an object, such as a celestial body, is the energy required to expand the material to infinity.	If a body with the mass and radius of Earth were made purely of hydrogen-1, then the gravitational binding energy of that body would be about 0.391658 eV per atom. If a hydrogen-1 body had the mass and radius of the Sun, its gravitational binding energy would be about 1,195.586 eV per atom.	Astrophysical level
Bond energy; Bond-dissociation energy	Bond energy and bond-dissociation energy are measures of the binding energy between the atoms in a chemical bond. It is the energy required to disassemble a molecule into its constituent atoms. This energy appears as chemical energy, such as that released in chemical explosions, the burning of chemical fuel and biological processes. Bond energies and bond-dissociation energies are typically in the range of a few eV per bond.	The bond-dissociation energy of a carbon-carbon bond is about 3.6 eV.	Molecular level
Electron binding energy; Ionization energy	Electron binding energy, more commonly known as ionization energy,^[3] is a measure of the energy required to free an electron from its atomic orbital or from a solid. The electron binding energy derives from the electromagnetic interaction of the electron with the nucleus and the other electrons of the atom, molecule or solid and is mediated by photons.	Among the chemical elements, the range of ionization energies is from 3.8939 eV for the outermost electron in an atom of caesium to 11.567617 keV for the innermost electron in an atom of copper.	Atomic level
Atomic binding energy	The atomic binding energy of the atom is the energy required to disassemble an atom into free electrons and a nucleus.^[4] It is the sum of the ionization energies of all the electrons belonging to a specific atom. The atomic binding energy derives from the electromagnetic interaction of the electrons with the nucleus, mediated by photons.	For an atom of helium, with 2 electrons, the atomic binding energy is the sum of the energy of first ionization (24.587 eV) and the energy of second ionization (54.418 eV), for a total of 79.005 eV.	Atomic level
Nuclear binding energy	Nuclear binding energy is the energy required to disassemble a nucleus into the free, unbound neutrons and protons it is composed of. It is the energy equivalent of the mass defect, the difference between the mass number of a nucleus and its measured mass.^[5]^[6] Nuclear binding energy derives from the nuclear force or residual strong force, which is mediated by three types of mesons.	The average nuclear binding energy per nucleon ranges from 1.11226 MeV for hydrogen-2 to 8.7945 MeV for nickel-62.	Nuclear level
Quantum chromodynamics binding energy	Quantum chromodynamics binding energy is misusing the denomination of a lack of energy. It addresses the mass and kinetic energy of the parts that bind the various quarks together inside a hadron. This energy derives from the strong interaction, which is mediated by gluons through virtual gluons and sea quarks.	The chromodynamic binding energy inside a nucleon amounts to approximately 99% of the nucleon's mass. The chromodynamic binding energy of a proton is about 928.9 MeV, while that of a neutron is about 927.7 MeV. Large binding energy between bottom quarks (280 MeV) causes some (theoretically expected) reactions with lambda baryons to release 138 MeV per event.^[7]	Elementary particle level

Mass–energy relation

A bound system is typically at a lower energy level than its unbound constituents because its mass must be less than the total mass of its unbound constituents. For systems with low binding energies, this "lost" mass after binding may be fractionally small, whereas for systems with high binding energies, the missing mass may be an easily measurable fraction. This missing mass may be lost during the process of binding as energy in the form of heat or light, with the removed energy corresponding to the removed mass through Einstein's equation $E = mc 2$ . In the process of binding, the constituents of the system might enter higher energy states of the nucleus/atom/molecule while retaining their mass, and because of this, it is necessary that they are removed from the system before its mass can decrease. Once the system cools to normal temperatures and returns to ground states regarding energy levels, it will contain less mass than when it first combined and was at high energy. This loss of heat represents the "mass deficit", and the heat itself retains the mass that was lost (from the point of view of the initial system). This mass will appear in any other system that absorbs the heat and gains thermal energy.^[8]

For example, if two objects are attracting each other in space through their gravitational field, the attraction force accelerates the objects, increasing their velocity, which converts their potential energy (gravity) into kinetic energy. When the particles either pass through each other without interaction or elastically repel during the collision, the gained kinetic energy (related to speed) begins to revert into potential energy, driving the collided particles apart. The decelerating particles will return to the initial distance and beyond into infinity, or stop and repeat the collision (oscillation takes place). This shows that the system, which loses no energy, does not combine (bind) into a solid object, parts of which oscillate at short distances. Therefore, to bind the particles, the kinetic energy gained due to the attraction must be dissipated by resistive force. Complex objects in collision ordinarily undergo inelastic collision, transforming some kinetic energy into internal energy (heat content, which is atomic movement), which is further radiated in the form of photons –the light and heat. Once the energy to escape the gravity is dissipated in the collision, the parts will oscillate at a closer, possibly atomic, distance, thus looking like one solid object. This lost energy, necessary to overcome the potential barrier to separate the objects, is the binding energy. If this binding energy were retained in the system as heat, its mass would not decrease, whereas binding energy lost from the system as heat radiation would itself have mass. It directly represents the "mass deficit" of the cold, bound system.

Closely analogous considerations apply in chemical and nuclear reactions. Exothermic chemical reactions in closed systems do not change mass, but do become less massive once the heat of reaction is removed, though this mass change is too small to measure with standard equipment. In nuclear reactions, the fraction of mass that may be removed as light or heat, i.e. binding energy, is often a much larger fraction of the system mass. It may thus be measured directly as a mass difference between rest masses of reactants and (cooled) products. This is because nuclear forces are comparatively stronger than the Coulombic forces associated with the interactions between electrons and protons that generate heat in chemistry.

Mass change

Mass change (decrease) in bound systems, particularly atomic nuclei, has also been termed mass defect, mass deficit, or mass packing fraction.^{[ citation needed ]}

The difference between the unbound system calculated mass and experimentally measured mass of nucleus (mass change) is denoted as Δm. It can be calculated as follows:

Mass change = (unbound system calculated mass) − (measured mass of system)

e.g. (sum of masses of protons and neutrons) − (measured mass of nucleus)

After a nuclear reaction occurs that results in an excited nucleus, the energy that must be radiated or otherwise removed as binding energy in order to decay to the unexcited state may be in one of several forms. This may be electromagnetic waves, such as gamma radiation; the kinetic energy of an ejected particle, such as an electron, in internal conversion decay; or partly as the rest mass of one or more emitted particles, such as the particles of beta decay. No mass deficit can appear, in theory, until this radiation or this energy has been emitted and is no longer part of the system.

When nucleons bind together to form a nucleus, they must lose a small amount of mass, i.e. there is a change in mass to stay bound. This mass change must be released as various types of photon or other particle energy as above, according to the relation $E = mc 2$ . Thus, after the binding energy has been removed, binding energy = mass change × $c 2$ . This energy is a measure of the forces that hold the nucleons together. It represents energy that must be resupplied from the environment for the nucleus to be broken up into individual nucleons.

For example, an atom of deuterium has a mass defect of 0.0023884 Da, and its binding energy is nearly equal to 2.23 MeV. This means that energy of 2.23 MeV is required to disintegrate an atom of deuterium.

The energy given off during either nuclear fusion or nuclear fission is the difference of the binding energies of the "fuel", i.e. the initial nuclide(s), from that of the fission or fusion products. In practice, this energy may also be calculated from the substantial mass differences between the fuel and products, which uses previous measurements of the atomic masses of known nuclides, which always have the same mass for each species. This mass difference appears once evolved heat and radiation have been removed, which is required for measuring the (rest) masses of the (non-excited) nuclides involved in such calculations.

Related Research Articles

Atoms are the basic particles of the chemical elements. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. Atoms with the same number of protons but a different number of neutrons are called isotopes of the same element.

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 Da. For example, uranium-238 decays to form thorium-234.

In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which an atomic nucleus emits a beta particle, transforming into an isobar of that nuclide. 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.

The neutron is a subatomic particle, symbol n or n⁰
, which has a neutral 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, they are both referred to as nucleons. Nucleons have a mass of approximately one atomic mass unit, or dalton, symbol Da. Their properties and interactions are described by nuclear physics. Protons and neutrons are not elementary particles; each is composed of three quarks.

<span class="mw-page-title-main">Nuclear physics</span> Field of physics that studies atomic nuclei

Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter.

Nuclear fusion is a reaction in which two or more atomic nuclei, usually deuterium and tritium, combine to form one or more different atomic nuclei and subatomic particles. The difference in mass between the reactants and products is manifested as either the release or absorption of energy. This difference in mass arises due to the difference in nuclear binding energy between the atomic nuclei before and after the reaction. Nuclear fusion is the process that powers active or main-sequence stars and other high-magnitude stars, where large amounts of energy are released.

In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number.

Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller 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 nuclear physics and nuclear chemistry, a nuclear reaction is a process in which two nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. 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.

<span class="mw-page-title-main">Mass number</span> Number of heavy particles in the atomic nucleus

The mass number (symbol A, from the German word: Atomgewicht, "atomic weight"), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approximately equal to the atomic (also known as isotopic) mass of the atom expressed in atomic mass units. Since protons and neutrons are both baryons, the mass number A is identical with the baryon number B of the nucleus (and also of the whole atom or ion). The mass number is different for each isotope of a given chemical element, and the difference between the mass number and the atomic number Z gives the number of neutrons (N) in the nucleus: N = A − Z.

<span class="mw-page-title-main">Nuclear force</span> Force that acts between the protons and neutrons of atoms

The nuclear force is a force that acts between hadrons, most commonly observed between protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nuclear force almost identically. Since protons have charge +1 e, they experience an electric force that tends to push them apart, but at short range the attractive nuclear force is strong enough to overcome the electrostatic force. The nuclear force binds nucleons into atomic nuclei.

<span class="mw-page-title-main">Nuclear binding energy</span> Minimum energy required to separate particles within a nucleus

Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the strong nuclear force. In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what the binding energy means.

The mass excess of a nuclide is the difference between its actual mass and its mass number in daltons. It is one of the predominant methods for tabulating nuclear mass. The mass of an atomic nucleus is well approximated by its mass number, which indicates that most of the mass of a nucleus arises from mass of its constituent protons and neutrons. Thus, the mass excess is an expression of the nuclear binding energy, relative to the binding energy per nucleon of carbon-12. If the mass excess is negative, the nucleus has more binding energy than ¹²C, and vice versa. If a nucleus has a large excess of mass compared to a nearby nuclear species, it can radioactively decay, releasing energy.

<span class="mw-page-title-main">Valley of stability</span> Characterization of nuclide stability

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.

Nickel-62 is an isotope of nickel having 28 protons and 34 neutrons.

The atomic mass (m_a or m) is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1 Da is defined as 1⁄12 of the mass of a free carbon-12 atom at rest in its ground state. The protons and neutrons of the nucleus account for nearly all of the total mass of atoms, with the electrons and nuclear binding energy making minor contributions. Thus, the numeric value of the atomic mass when expressed in daltons has nearly the same value as the mass number. Conversion between mass in kilograms and mass in daltons can be done using the atomic mass constant $.$

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.

<span class="mw-page-title-main">Nuclear drip line</span> Atomic nuclei decay delimiter

The nuclear drip line is the boundary beyond which atomic nuclei are unbound with respect to the emission of a proton or neutron.

<span class="mw-page-title-main">Discovery of the neutron</span> Scientific background leading to the discovery of subatomic particles

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, isotopes of chemical elements 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.

<span class="mw-page-title-main">Separation energy</span> Energy needed to remove a specified particle from an atoms nucleus

In nuclear physics, separation energy is the energy needed to remove one nucleon from an atomic nucleus.

References

↑ Rohlf, James William (1994). Modern Physics from α to Z°. John Wiley & Sons. p. 20. ISBN 0471572705.
↑ Eisberg, Robert; Resnick, Robert (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (2nd ed.). John Wiley & Sons. p. 524. ISBN 047187373X.
↑ IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " Ionization energy ". doi : 10.1351/goldbook.I03199
↑ "Binding Energy". Nuclear Power. Retrieved 16 May 2015.
↑ Bodansky, David (2005). Nuclear Energy: Principles, Practices, and Prospects (2nd ed.). New York: Springer Science + Business Media, LLC. p. 625. ISBN 9780387269313.
↑ Wong, Samuel S.M. (2004). Introductory nuclear physics (2nd ed.). Weinheim: Wiley-VCH. pp. 9–10. ISBN 9783527617913.
↑ Karliner, Marek, and Jonathan L. Rosner. "Quark-level analogue of nuclear fusion with doubly heavy baryons". Nature 551.7678 (2017): 89.
↑ E. F. Taylor and J. A. Wheeler, Spacetime Physics, W.H. Freeman and Co., NY. 1992. ISBN 0716723271, see pp. 248–249 for discussion of mass remaining constant after detonation of nuclear bombs until heat is allowed to escape.

External links

Nuclear Binding Energy
Mass and Nuclide Stability
Experimental atomic mass data compiled Nov. 2003 Archived 2008-09-23 at the Wayback Machine

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[1] Rohlf, James William (1994). Modern Physics from α to Z°. John Wiley & Sons. p. 20. ISBN 0471572705.

[2] Eisberg, Robert; Resnick, Robert (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (2nd ed.). John Wiley & Sons. p. 524. ISBN 047187373X.

[3] IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " Ionization energy ". doi : 10.1351/goldbook.I03199

[nuclearpower-4] "Binding Energy". Nuclear Power. Retrieved 16 May 2015.

[5] Bodansky, David (2005). Nuclear Energy: Principles, Practices, and Prospects (2nd ed.). New York: Springer Science + Business Media, LLC. p. 625. ISBN 9780387269313.

[6] Wong, Samuel S.M. (2004). Introductory nuclear physics (2nd ed.). Weinheim: Wiley-VCH. pp. 9–10. ISBN 9783527617913.

[7] Karliner, Marek, and Jonathan L. Rosner. "Quark-level analogue of nuclear fusion with doubly heavy baryons". Nature 551.7678 (2017): 89.

[8] E. F. Taylor and J. A. Wheeler, Spacetime Physics, W.H. Freeman and Co., NY. 1992. ISBN 0716723271, see pp. 248–249 for discussion of mass remaining constant after detonation of nuclear bombs until heat is allowed to escape.

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