Nuclear Binding Energy

A binding energy is generally the energy required to disassemble a whole system into separate parts. It is known the sum of separate parts has typically a higher potential energy than a bound system, therefore the bound system is more stable. A creation of bound system is often accompanied by subsequent energy release. We usually distinguish the binding energy according to these levels:

  • Atomic level
  • Molecular level
  • Nuclear level
At nuclear level the nuclear binding energy is the energy required to disassemble (to overcome the strong nuclear force) a nucleus of an atom into its component parts (protons and neutrons). The protons and neutrons in an atomic nucleus are held together by the nuclear forces (strong force). The mass of a nucleus is always less than the sum of masses of the constituent protons and neutrons when separated. The difference is a measure of the nuclear binding energy (Eb) which holds the nucleus together. According to the Einstein relationship (E=m.c2) this binding energy is proportional to this mass difference and it is known as the mass defect.

Nuclear binding energy curve.

Nuclear binding energy curve.
Source: hyperphysics.phy-astr.gsu.edu

During the nuclear splitting or nuclear fusion, some of the mass of the nucleus gets converted into huge amounts of energy and thus this mass is removed from the total mass of the original particles, and the mass is missing in the resulting nucleus. The nuclear binding energies are enormous, they are on the order of a million times greater than the electron binding energies of atoms.

For a nucleus with A (mass number) nucleons, the binding energy per nucleon Eb/A can be calculated. This calculated fraction is shown in the chart as a function of them mass number A. As can be seen, for low mass numbers Eb/A increases rapidly and reaches a maximum of 8.8 MeV at approximately A=60. The nuclei with the highest binding energies, that are most tightly bound belong to the “iron group” of isotopes (56Fe, 58Fe, 62Ni). After that, the binding energy per nucleon decreases. In the heavy nuclei (A>60) region, a more stable configuration is obtained, when a heavy nucleus splits into two lighter nuclei. This is the origin of the fission process. It may seem that all the heavy nuclei may undergo fission or even spontaneous fission. In fact, for all nuclei with atomic number greater than about 60, fission occurs very rarely. In order to fission process to take place, a sufficient amount of energy must be added to the nucleus and no matter how. The energetics and binding energies of certain nucleus are well described by the Liquid Drop Model, which examines the global properties of nuclei.

See also: Nuclear Binding Curve

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