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(also separation energy), the energy of any bound system of particles (such as an atom) equal to the work required to decompose the system into constituent particles such that they are an infinite distance from each other and cannot interact. It is a negative quantity, since energy is released in the course of the formation of the bound state, and its absolute value characterizes the bond strength (for example, the stability of nuclei).
According to the Einstein relation, the binding energy is equivalent to the mass defect Δm: ΔE = Δmc2, where c is the velocity of light in a vacuum (seeMASS DEFECT). It is determined by the type of interaction between the particles in a given system. Thus, the binding energy of the nucleus is due to the strong interactions of the nucleons in the nucleus (in the more stable nuclei of intermediate atoms, the specific binding energy is ~8 × 106 electron volts [eV]). The energy may be released when light nuclei fuse into heavier ones, as well as upon the fission of heavy nuclei, which is explained by the decrease of the specific binding energy with increasing atomic number.
The binding energy of electrons in an atom or molecule is determined by the electromagnetic interactions, and for each electron it is proportional to the ionization potential; it is equal to 13.6 eV for an electron of the hydrogen atom in the normal state. These same interactions are responsible for the binding energy of atoms in a molecule or crystal. In the case of the gravitational interaction, the binding energy is ordinarily small; however, it may be of considerable magnitude for certain celestial objects, such as black holes.