Nuclear binding energy

(nuclear physics) The energy required to separate an atom into its constituent protons, neutrons, and electrons.

The amount by which the mass of an atom is less than the sum of the masses of its constituent protons, neutrons, and electrons expressed in units of energy. This energy difference accounts for the stability of the atom. In principle, the binding energy is the amount of energy which was released when the several atomic constituents came together to form the atom. Most of the binding energy is associated with the nuclear constituents (protons and neutrons), or nucleons, and it is customary to regard this quantity as a measure of the stability of the nucleus alone. See also Nuclear structure.

A widely used term, the binding energy (BE) per nucleon, is defined by the equation below, where _ZM^A represents the mass of an atom of mass number A and atomic number Z, H and n are the masses of the hydrogen atom and neutron, respectively, and c is the velocity of light. The binding energies of the orbital electrons, here practically neglected, are not only small, but increase with Z in a gradual manner; thus the BE/nucleon gives an accurate picture of the variations and tends in nuclear stability.

The binding energy, when expressed in mass units, is known as the mass defect, a term sometimes incorrectly applied to quantity M − A, where M is the mass of the atom. See also Mass defect.

The term binding energy is sometimes also used to describe the energy which must be supplied to a nucleus in order to remove a specified particle to infinity, for example, a neutron, proton, or alpha particle. A more appropriate term for this energy is the separation energy. This quantity varies greatly from nucleus to nucleus and from particle to particle. For example, the binding energies for a neutron, a proton, and a deuteron in ¹⁶O are 15.67, 12.13, and 20.74 MeV, respectively, while the corresponding energies in ¹⁷O are 4.14, 13.78, and 14.04 MeV, respectively. The usual order of neutron or proton separation energy is 7–9 MeV for most of the periodic table.