Binding energy
Encyclopedia
Binding energy is the mechanical energy
required to disassemble a whole into separate parts. A bound system
typically has a lower potential energy
than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state. The usual convention is that this corresponds to a positive binding energy.
which must be done against the forces which hold an object together, disassembling the object into component parts separated by sufficient distance that further separation requires negligible additional work.
At the atomic level
the atomic binding energy of the atom derives from electromagnetic interaction and is the energy
required to disassemble an atom into free electrons and a nucleus. Electron binding energy is a measure of the energy required to free electrons from their atomic orbits. This is more commonly known as ionization energy
.
At the nuclear level
, binding energy is also equal to the energy liberated when a nucleus is created from other nucleons or nuclei. This nuclear binding energy (binding energy of nucleon
s into a nuclide
) is derived from the strong nuclear force and is the energy
required to disassemble a nucleus
into the same number of free unbound neutron
s and proton
s it is composed of, so that the nucleons are far/distant enough from each other so that the strong nuclear force can no longer cause the particles to interact.
In astrophysics
, gravitational binding energy
of a celestial body is the energy required to expand the material to infinity. This quantity is not to be confused with the gravitational potential energy, which is the energy required to separate two bodies, such as a celestial body and a satellite, to infinite distance, keeping each intact (the latter energy is lower).
In bound systems, if the binding energy is removed from the system, it must be subtracted from the mass
of the unbound system, simply because this energy has mass, and if subtracted from the system at the time it is bound, will result in removal of mass from the system. System mass is not conserved in this process because the system is not closed during the binding process.
Since all forms of energy exhibit rest mass within systems at "rest"
(that is, systems which have no net momentum), the question of where the missing mass of the binding energy goes, is of interest. The answer is that this mass is lost from a system which is not closed. It transforms to heat, light, higher energy states of the nucleus/atom or other forms of energy, but these types of energy also have mass, and it is necessary that they be removed from the system before its mass may decrease. The "mass deficit" from binding energy is therefore removed mass that corresponds with removed energy, according to Einstein's equation E = mc2. Once the system cools to normal temperatures and returns to ground states in terms of energy levels, there is less mass remaining in the system than there was when it first combined and was at high energy. Mass measurements are almost always made at low temperatures with systems in ground states, and this difference between the mass of a system and the sum of the masses of its isolated parts is called a mass deficit. Thus, if binding energy mass is transformed into heat, the system must be cooled (the heat removed) before the mass-deficit appears in the cooled system. In that case, the removed heat represents exactly the mass "deficit", and the heat itself retains the mass which was lost (from the point of view of the initial system). This mass appears in any other system which absorbs the heat and gains thermal energy.
As an illustration, consider two objects attracting each other in space through their gravitational field
. The attraction force accelerates the objects and they gain some speed toward each other converting the potential (gravity) energy into kinetic (movement) energy. When either the particles 1) pass through each other without interaction or 2) elastically repel during the collision, the gained kinetic energy (related to speed), starts to revert into potential form 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, in order 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 closer, possibly atomic, distance, thus looking like one solid object. This lost energy, necessary to overcome the potential barrier in order to separate the objects, is the binding energy. If this binding energy were retained in the system as heat, its mass would not decrease. However, binding energy lost from the system (as heat radiation) would itself have mass, and directly represents the "mass deficit" of the cold, bound system.
Closely analogous considerations apply in chemical and nuclear considerations. Exothermic chemical reactions in closed systems do not change mass, but (in theory) become less massive once the heat of reaction is removed. This mass change is too small to measure with standard equipment. In nuclear reactions, however, 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 products. This is because nuclear forces are comparatively stronger than Coulombic forces associated with the interactions between electrons and protons that generate heat in chemistry.
In nuclear reactions, the energy that must be radiated
or otherwise removed as binding energy may be in the form of electromagnetic waves, such as gamma radiation, or as heat. Again, however, no mass deficit can in theory appear until this radiation has been emitted and is no longer part of the system.
The energy given off during either nuclear fusion
or nuclear fission
is the difference between the binding energies of the fuel and the fusion or fission products. In practice, this energy may also be calculated from the substantial mass differences between the fuel and products, once evolved heat and radiation have been removed.
When the nucleons are grouped together to form a nucleus, they lose a small amount of mass, i.e., there is mass defect. This mass defect is released as (often radiant) energy according to the relation E = mc2; thus
binding energy = mass defect × c2.
This energy is a measure of the forces that hold the nucleons together, and it represents energy which must be supplied from the environment if the nucleus is to be broken up. It is known as binding energy, and the mass defect is a measure of the binding energy because it simply represents the mass of the energy which has been lost to the environment after binding.
In 2005, Rainville et al. published a direct test of the energy-equivalence of mass lost in the binding-energy of a neutron to atoms of particular isotopes of silicon and sulfur, by comparing the new mass-defect to the energy of the emitted gamma ray associated with the neutron capture. The binding mass-loss agreed with the gamma ray energy to a precision of ±0.00004 %, the most accurate test of E=mc2 to date.
. This difference is called mass excess.
The difference between the actual mass of the nucleus measured in atomic mass units and the number of nucleons is called mass excess i.e.
Mass excess
= M - A = Excess-energy / c2
with : M equals the actual mass of the nucleus, in u.
and : A equals the mass number
.
This mass excess is a practical value calculated from experimentally measured nucleon masses and stored in nuclear databases. For middle-weight nuclides this value is negative in contrast to the mass defect which is never negative for any nuclide.
Mechanical energy
In physics, mechanical energy is the sum of potential energy and kinetic energy present in the components of a mechanical system. It is the energy associated with the motion and position of an object. The law of conservation of energy states that in an isolated system that is only subject to...
required to disassemble a whole into separate parts. A bound system
Bound state
In physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space...
typically has a lower potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...
than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state. The usual convention is that this corresponds to a positive binding energy.
General
In general, binding energy represents the mechanical workMechanical work
In physics, work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force. Only the component of a force in the direction of the movement of its point of application does work...
which must be done against the forces which hold an object together, disassembling the object into component parts separated by sufficient distance that further separation requires negligible additional work.
At the atomic level
Quantum chemistry
Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems...
the atomic binding energy of the atom derives from electromagnetic interaction and is the energy
Ionization energy
The ionization energy of a chemical species, i.e. an atom or molecule, is the energy required to remove an electron from the species to a practically infinite distance. Large atoms or molecules have a low ionization energy, while small molecules tend to have higher ionization energies.The property...
required to disassemble an atom into free electrons and a nucleus. Electron binding energy is a measure of the energy required to free electrons from their atomic orbits. This is more commonly known as ionization energy
Ionization energy
The ionization energy of a chemical species, i.e. an atom or molecule, is the energy required to remove an electron from the species to a practically infinite distance. Large atoms or molecules have a low ionization energy, while small molecules tend to have higher ionization energies.The property...
.
At the nuclear level
Nuclear physics
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
, binding energy is also equal to the energy liberated when a nucleus is created from other nucleons or nuclei. This nuclear binding energy (binding energy of nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
s into a nuclide
Nuclide
A nuclide is an atomic species characterized by the specific constitution of its nucleus, i.e., by its number of protons Z, its number of neutrons N, and its nuclear energy state....
) is derived from the strong nuclear force and is the energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
required to disassemble a nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
into the same number of free unbound neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
s and proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
s it is composed of, so that the nucleons are far/distant enough from each other so that the strong nuclear force can no longer cause the particles to interact.
In astrophysics
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
, gravitational binding energy
Gravitational binding energy
The gravitational binding energy of an object consisting of loose material, held together by gravity alone, is the amount of energy required to pull all of the material apart, to infinity...
of a celestial body is the energy required to expand the material to infinity. This quantity is not to be confused with the gravitational potential energy, which is the energy required to separate two bodies, such as a celestial body and a satellite, to infinite distance, keeping each intact (the latter energy is lower).
In bound systems, if the binding energy is removed from the system, it must be subtracted from the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
of the unbound system, simply because this energy has mass, and if subtracted from the system at the time it is bound, will result in removal of mass from the system. System mass is not conserved in this process because the system is not closed during the binding process.
Mass deficit
Classically a bound system is at a lower energy level than its unbound constituents, and 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. For systems with high binding energies, however, the missing mass may be an easily measurable fraction.Since all forms of energy exhibit rest mass within systems at "rest"
Mass-energy equivalence
In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant...
(that is, systems which have no net momentum), the question of where the missing mass of the binding energy goes, is of interest. The answer is that this mass is lost from a system which is not closed. It transforms to heat, light, higher energy states of the nucleus/atom or other forms of energy, but these types of energy also have mass, and it is necessary that they be removed from the system before its mass may decrease. The "mass deficit" from binding energy is therefore removed mass that corresponds with removed energy, according to Einstein's equation E = mc2. Once the system cools to normal temperatures and returns to ground states in terms of energy levels, there is less mass remaining in the system than there was when it first combined and was at high energy. Mass measurements are almost always made at low temperatures with systems in ground states, and this difference between the mass of a system and the sum of the masses of its isolated parts is called a mass deficit. Thus, if binding energy mass is transformed into heat, the system must be cooled (the heat removed) before the mass-deficit appears in the cooled system. In that case, the removed heat represents exactly the mass "deficit", and the heat itself retains the mass which was lost (from the point of view of the initial system). This mass appears in any other system which absorbs the heat and gains thermal energy.
As an illustration, consider two objects attracting each other in space through their gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
. The attraction force accelerates the objects and they gain some speed toward each other converting the potential (gravity) energy into kinetic (movement) energy. When either the particles 1) pass through each other without interaction or 2) elastically repel during the collision, the gained kinetic energy (related to speed), starts to revert into potential form 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, in order 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
Inelastic collision
An inelastic collision, in contrast to an elastic collision, is a collision in which kinetic energy is not conserved.In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed.The molecules of a gas...
, 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 closer, possibly atomic, distance, thus looking like one solid object. This lost energy, necessary to overcome the potential barrier in order to separate the objects, is the binding energy. If this binding energy were retained in the system as heat, its mass would not decrease. However, binding energy lost from the system (as heat radiation) would itself have mass, and directly represents the "mass deficit" of the cold, bound system.
Closely analogous considerations apply in chemical and nuclear considerations. Exothermic chemical reactions in closed systems do not change mass, but (in theory) become less massive once the heat of reaction is removed. This mass change is too small to measure with standard equipment. In nuclear reactions, however, 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 products. This is because nuclear forces are comparatively stronger than Coulombic forces associated with the interactions between electrons and protons that generate heat in chemistry.
Mass defect
The difference between the unbound system calculated mass and experimentally measured mass of nucleus is called mass defect. It is denoted by Δm. It can be calculated as follows:- Mass defect = (unbound system calculated mass) - (measured mass of nucleus)
- i.e, (sum of masses of protons and neutrons) - (measured mass of nucleus)
In nuclear reactions, the energy that must be radiated
Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...
or otherwise removed as binding energy may be in the form of electromagnetic waves, such as gamma radiation, or as heat. Again, however, no mass deficit can in theory appear until this radiation has been emitted and is no longer part of the system.
The energy given off during either nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
or nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...
is the difference between the binding energies of the fuel and the fusion or fission products. In practice, this energy may also be calculated from the substantial mass differences between the fuel and products, once evolved heat and radiation have been removed.
When the nucleons are grouped together to form a nucleus, they lose a small amount of mass, i.e., there is mass defect. This mass defect is released as (often radiant) energy according to the relation E = mc2; thus
binding energy = mass defect × c2.
This energy is a measure of the forces that hold the nucleons together, and it represents energy which must be supplied from the environment if the nucleus is to be broken up. It is known as binding energy, and the mass defect is a measure of the binding energy because it simply represents the mass of the energy which has been lost to the environment after binding.
In 2005, Rainville et al. published a direct test of the energy-equivalence of mass lost in the binding-energy of a neutron to atoms of particular isotopes of silicon and sulfur, by comparing the new mass-defect to the energy of the emitted gamma ray associated with the neutron capture. The binding mass-loss agreed with the gamma ray energy to a precision of ±0.00004 %, the most accurate test of E=mc2 to date.
Mass excess
It is observed experimentally that the mass of the nucleus is smaller than the number of nucleons each counted with a mass of 1 a.m.u.Atomic mass unit
The unified atomic mass unit or dalton is a unit that is used for indicating mass on an atomic or molecular scale. It is defined as one twelfth of the rest mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state, and has a value of...
. This difference is called mass excess.
The difference between the actual mass of the nucleus measured in atomic mass units and the number of nucleons is called mass excess i.e.
Mass excess
Mass excess
The mass excess of a nuclide is the difference between its actual mass and its mass number in atomic mass units. 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...
= M - A = Excess-energy / c2
with : M equals the actual mass of the nucleus, in u.
and : A equals the mass number
Mass number
The mass number , also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. 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...
.
This mass excess is a practical value calculated from experimentally measured nucleon masses and stored in nuclear databases. For middle-weight nuclides this value is negative in contrast to the mass defect which is never negative for any nuclide.
See also
- Mass excessMass excessThe mass excess of a nuclide is the difference between its actual mass and its mass number in atomic mass units. 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...
- 56FeIron-56Iron-56 is the most common isotope of iron. About 91.754% of all iron is iron-56.Of all isotopes, iron-56 has the lowest mass per nucleon. With 8.8 MeV binding energy per nucleon, iron-56 is one of the most tightly bound nuclei....
- Semi-empirical mass formulaSemi-empirical mass formulaIn nuclear physics, the semi-empirical mass formula is used to approximate the mass and various other properties of an atomic nucleus...
- Electron binding energy
- Chemical bondChemical bondA chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...
- Bond energyBond energyIn chemistry, bond energy is the measure of bond strength in a chemical bond. It is the heat required to break one Mole of molecules into their individual atoms. For example, the carbon-hydrogen bond energy in methane E is the enthalpy change involved with breaking up one molecule of methane into...
- Nuclear fissionNuclear fissionIn nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...
- Nuclear fusionNuclear fusionNuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
- Nuclear reactionNuclear reactionIn 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 from outside the atom, collide to produce products different from the initial particles...
- Strong nuclear force
- William ProutWilliam ProutWilliam Prout FRS was an English chemist, physician, and natural theologian. He is remembered today mainly for what is called Prout's hypothesis.-Biography:...
