digplanet beta 1: Athena
Share digplanet:


Applied sciences






















Binding energy is the energy required to disassemble a whole system into separate parts. A bound system typically has a lower potential energy than the sum of its constituent parts — this is what keeps the system together. Often this means that energy is released upon the creation of a bound state. This definition corresponds to a positive binding energy. (This definition also often causes confusion. For example: A prominent term in chemistry is the 'free energy of binding', which is the difference between the bound and unbound states and thus negative).

General idea[edit]

In general, binding energy represents the mechanical work that 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.[1]

At the nuclear level, binding energy is also equal to the energy liberated when a nucleus is created from other nucleons or nuclei.[2][3] This nuclear binding energy (binding energy of nucleons into a nuclide) is derived from the nuclear force (residual strong interaction) and is the energy required to disassemble a nucleus into the same number of free, unbound neutrons and protons it is composed of, so that the nucleons are far/distant enough from each other so that the nuclear force can no longer cause the particles to interact.[4]

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. Thus, if energy is removed (or emitted) from the system at the time it is bound, the loss of energy from the system will also result in the loss of the mass of the energy, from the system.[5] System mass is not conserved in this process because the system is "open" (i.e., is not an isolated system to mass or energy input or loss) during the binding process.

Mass-energy relation[edit]

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" (that is, in 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.[6]

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 become less massive once the heat of reaction is removed, though this mass change is much 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 (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[edit]

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 by Δm. It can be calculated as follows:

Mass change = (unbound system calculated mass) - (measured mass of system)
i.e., (sum of masses of protons and neutrons) - (measured mass of nucleus)

After nuclear reactions that result in an excited nucleus, the energy that must be radiated or otherwise removed as binding energy for a single nucleus may be in the form of electromagnetic waves, such as gamma radiation, or it may appear in the kinetic energy of an ejected particle, such as an electron, in internal conversion decay. Also, energy of excitation of nucleus can be partly emitted as the rest mass of one or more a particle, such as the emitted particles of beta decay. Again, however, no mass deficit can in theory appear 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 mass change, in order 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 = mc2. Thus, after binding energy has been removed, binding energy = mass change × c2. This energy is a measure of the forces that hold the nucleons together, and it represents energy which must be supplied again from the environment, if the nucleus were to be broken up into individual nucleons.

The energy given off during either nuclear fusion or nuclear fission is the difference between the binding energies of the "fuel", i.e., the initial nuclide(s), and 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 measurement 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 a given requirement for measuring the (rest) masses of the (non-excited) nuclides involved in such calculations.

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-change 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.[7]

Excess mass[edit]

Main article: 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.. 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 change which is never negative for any nuclide.

Nuclear binding energy[edit]

Electron binding energy[edit]

Gravitational binding energy[edit]

Bond energy[edit]

Main article: Bond energy

See also[edit]


  1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Ionization energy".
  2. ^ Brittanica Online Encyclopaedia - "nuclear binding energy". Accessed 8 September 2010. http://www.britannica.com/EBchecked/topic/65615/binding-energy
  3. ^ Nuclear Engineering - "Binding Energy". Bill Garland, McMaster University. Accessed 8 September 2010. http://www.nuceng.ca/igna/binding_energy.htm
  4. ^ Atomic Alchemy: Nuclear Processes - "Binding Energy". About. Accessed 7 September 2010. http://library.thinkquest.org/17940/texts/binding_energy/binding_energy.html
  5. ^ HyperPhysics - "Nuclear Binding Energy". C.R. Nave, Georgia State University. Accessed 7 September 2010. http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html
  6. ^ E. F. Taylor and J. A. Wheeler, Spacetime Physics, W.H. Freeman and Co., NY. 1992. ISBN 0-7167-2327-1, see pp. 248-9 for discussion of mass remaining constant after detonation of nuclear bombs, until heat is allowed to escape.
  7. ^ Rainville, S. et al. World Year of Physics: A direct test of E=mc2. Nature 438, 1096-1097 (22 December 2005) | doi:10.1038/4381096a; Published online 21 December 2005.

External links[edit]

Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Binding_energy — Please support Wikipedia.
This page uses Creative Commons Licensed content from Wikipedia. A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
308816 videos foundNext > 

E=MC^2, Binding Energy and Mass Defect

http://www.aklectures.com/lecture/e-mc-2-binding-energy-and-mass-defect The website organizes the videos into clear and structured chapters that you can use ...

Mass defect and binding energy (1)

Physics: Nuclear physics--mass defect and binding energy. This is a recording of a tutoring session, posted with the student's permission. These videos are o...

Mass defect and binding energy

How to calculate the mass defect and binding energy for helium-4 More free lessons at: http://www.khanacademy.org/video?v=9b8qZ6OHZ5s.

Binding Energy, Fission and the Strong Nuclear Force

Cassiopeia Project http://www.cassiopeiaproject.com/ St. Mary's Physics Online http://www.stmary.ws/highschool/physics/home/notes/modPhysics/ForcesInsideNucl...

Binding Energy and Fission

This movie is part of the collection: Prelinger Archives Producer: Sutherland (John) Productions Sponsor: General Electric Company http://www.stmary.ws/highs...

Mass defect and Binding Energy

mass defect and binding energy and how this relates to Einstein's Famous formula.

Nuclear chemistry. Binding energy (1)

Chemistry: Nuclear chemistry. Atomic number, mass number. Mass defect and binding energy This is a recording of a tutoring session, posted with the students'...

IB Physics: Nuclear Binding Energy

Defines the amu, and explains how the binding energy can be calculated based on the mass defect, and determines the binding energy per nucleon of Helium-4.

Nuclear Binding Energy Calculation ; Mass Defect

this video uses E=mc^2 to determine the mass defect (mass difference) to calculate the nuclear binding Energy, E (energy difference). The nuclear binding ene...

Particle Physics - Binding Energy

What is the binding Energy (in MeV) for lithium, 7/3 Li, with an atomic mass of 7.016003 u?

308816 videos foundNext > 

305 news items


Tue, 21 Oct 2014 05:22:30 -0700

All the benefits outlined above can be reaped if Heads of State and Government as well as all other EU leaders would agree on 23rd October to adopt an ambitious, binding energy efficiency target reflecting the potential of the building sector. Research ...


Fri, 17 Oct 2014 04:16:56 -0700

The UK and Cyprus are against setting any binding energy efficiency targets, while Germany, Denmark and Portugal want all three targets binding and, for renewables and efficiency, set at 30%. Conclusions reached on the 23-24 October will inform the EU ...

Energy Live News - Energy Made Easy

Mon, 20 Oct 2014 03:18:45 -0700

Although many member states are signalling their support for a binding energy efficiency target of 30%, others, led by the UK and The Netherlands, are stating that the costs are too high, but this is based on flawed and censored information that ...


Mon, 20 Oct 2014 23:38:45 -0700

UK urged to drop opposition to binding energy efficiency target · Farage again denied key European Parliament posts · Farage's EFDD group in Parliament collapses · Barroso: UK cannot get by without a little help from its friends · EU to discuss ...


Mon, 20 Oct 2014 23:45:00 -0700

Poll: support for UKIP hits record high · UK urged to drop opposition to binding energy efficiency target · Farage again denied key European Parliament posts · Farage's EFDD group in Parliament collapses · Barroso: UK cannot get by without a little ...
Business Green
Mon, 20 Oct 2014 06:56:14 -0700

... reforms to the ETS would almost certainly lead to further calls from Eastern European states for financial sweeteners and could also have implications for the parallel negotiations on whether or not the bloc should agree a binding energy efficiency ...

pv magazine

pv magazine
Mon, 06 Oct 2014 03:23:03 -0700

The U.K., along with Poland, has consistently resisted efforts by the European Commission to impose binding energy reduction targets, citing that such a move would be bad for business. However, this modeling would appear to suggest that the opposite ...
Thomson Reuters Foundation (blog)
Thu, 16 Oct 2014 04:26:15 -0700

Not having a binding energy efficiency targets "will drive us to invest in other parts of the world," Barry Lynham, Director of Strategy for Knauf Insulation, an insulation company with production sites in Russia, Turkey, the Middle East and the United ...

Oops, we seem to be having trouble contacting Twitter

Support Wikipedia

A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia. Please add your support for Wikipedia!