binding energy
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In physics and chemistry, binding energy is the smallest amount of
energy In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical quantity, quantitative physical property, property that is #Energy transfer, transferred to a phy ...
required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. 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. A bound system is typically at a lower energy level than its unbound constituents. According to relativity theory, a decrease in the total energy of a system is accompanied by a decrease in the total mass, where .


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.


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 . 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.E. F. Taylor and J. A. Wheeler, ''Spacetime Physics'', W.H. Freeman and Co., NY. 1992. , see pp. 248–249 for discussion of mass remaining constant after detonation of nuclear bombs until heat is allowed to escape. For example, if two objects are attracting each other in space through their
gravitational field In physics, a gravitational field is a scientific model, model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational Field (physics), field is us ...
, 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 An inelastic collision, in contrast to an elastic collision, is a collision in which kinetic energy is not conserved due to the action of Friction#Internal friction, internal friction. In collisions of macroscopic bodies, some kinetic energy is t ...
, transforming some kinetic energy into internal energy (heat content, which is atomic movement), which is further radiated in the form of photonsthe 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 reaction In nuclear physics 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 physics should not be confused with atomic phy ...
s, 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 mass 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 A system is a group of interacting or interrelated elements that act according ...
es 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''. The difference between the unbound system calculated mass and experimentally measured mass of nucleus (mass change) is denoted as Δ''m''. 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 A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nucleus, atomic nuclei. It consists of the shortest wavelength electromagnetic wav ...
; the kinetic energy of an ejected particle, such as an electron, in
internal conversion Internal conversion is a non-radioactive, atomic decay process where an excited nucleus Nucleus (plural, : nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom * ...
decay; or partly as the rest mass of one or more emitted particles, such as the particles of
beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar (nuclide), isobar of that ...
. 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 . Thus, after the binding energy has been removed, binding energy = mass change × . 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 Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
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 Nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles ( neutrons or protons). The difference in mass between the reactants and products is mani ...
or
nuclear fission Nuclear fission is a nuclear reaction, reaction in which the atomic nucleus, nucleus of an atom splits into two or more smaller atomic nucleus, nuclei. The fission process often produces gamma ray, gamma photons, and releases a very large ...
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 mass The atomic mass (''m''a or ''m'') is the mass of an atom. Although the SI unit of mass is the kilogram (unit), kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (unit), dalton (symbol: Da) – equivalently, unif ...
es 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.


See also

*
Bond energy In chemistry, bond energy (''BE''), also called the mean bond enthalpy or average bond enthalpy is the measure of bond strength in a chemical bond. IUPAC defines bond energy as the average value of the gas-phase bond-dissociation energy (usually at ...
and
bond-dissociation energy The bond-dissociation energy (BDE, ''D''0, or ''DH°'') is one measure of the bond strength, strength of a chemical bond . It can be defined as the standard enthalpy change when is cleaved by homolysis (chemistry), homolysis to give fragments ...
*
Gravitational binding energy The gravitational binding energy of a system is the minimum energy which must be added to it in order for the system to cease being in a Gravity, gravitationally bound state. A gravitationally bound system has a lower (''i.e.'', more negative) Gr ...
*
Ionization energy Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive Electric charge, charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged a ...
(binding energy of one electron) *
Nuclear binding energy Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the atomic nucleus, nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable n ...
* Quantum chromodynamics binding energy *
Semi-empirical mass formula In nuclear physics 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 physics should not be confused with atomic physic ...
* Separation energy (binding energy of one nucleon) * Virial mass * Prout's hypothesis, an early model of the atom that did not account for
mass defect Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the atomic nucleus, nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable n ...


References


External links


Nuclear Binding EnergyExperimental atomic mass data compiled Nov. 2003
{{DEFAULTSORT:Binding Energy Energy (physics) Mass spectrometry Nuclear physics Forms of energy