Binding energy


General idea



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

Types of binding energy

In astrophysics, the gravitational binding energy of a celestial body is the energy required to expand the material to infinity. Solely for the purpose of comparison with the other types of binding energy, if a body with the mass and radius of the Earth were made purely of carbon-12, then the gravitational binding energy of that body would be about 4.66 eV per atom. If a carbon-12 body had the mass and radius of the Sun, its gravitational binding energy would be about 14.24 keV per atom.

At the molecular level, 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 few eV per bond. For example, the bond-dissociation energy of a carbon-carbon bond is about 3.6 eV.

At the atomic level, the atomic binding energy of the atom derives from electromagnetic interaction, mediated by photons. It is the energy required to disassemble an atom into free electrons and a nucleus.[2] 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.[3] Among the chemical elements, the range of ionization energies is from 3.8939 eV for the first electron in an atom of caesium to 11.567617 keV for the 29th electron in an atom of copper.

At the nuclear level, 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 excess, the difference between the mass number of a nucleus and its true measured mass.[4][5] 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 2.22452 MeV for hydrogen-2 to 8.7945 MeV for nickel-62.

At a yet more fundamental level, quantum chromodynamics binding energy is the energy which binds the various quarks together inside a hadron. This energy derives from the strong interaction, which is mediated by gluons. The chromodynamic binding energy inside a nucleon, for example, 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.

Mass-energy relation




Mass change


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)
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 to produce the unexcited state may be in any 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, 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. It represents energy that 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 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 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.

See also


  2. "Nuclear Power Binding Energy". Retrieved 16 May 2015.
  3. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006) "Ionization energy".
  4. Bodansky, David (2005). Nuclear Energy: Principles, Practices, and Prospects (2nd ed.). New York: Springer Science + Business Media, LLC. p. 625. ISBN 9780387269313.
  5. Wong, Samuel S.M. (2004). Introductory nuclear physics (2nd ed.). Weinheim: Wiley-VCH. pp. 910. ISBN 9783527617913.

External links
