Binding energy is the energy required to disassemble a whole into separate parts. A bound system has a lower potential energy than its constituent parts; this is what keeps the system together; it corresponds to a positive binding energy.

At the nuclear level, binding energy is derived from the strong nuclear force and is the energy required to disassemble a nucleus into neutrons and protons. At the atomic level, binding energy is derived from electromagnetic interaction and is the energy required to disassemble an atom into electrons and a nucleus. In astrophysics, gravitational binding energy of a celestial body is the energy required to disassemble it into space debris, not to be confused with the gravitational potential energy to separate e.g. a celestial body and a satellite to infinite distance, keeping each intact.

Because a bound system is at a lower energy level, its mass must be less than its unbound constituents. Nuclear binding energy can be computed from the difference in mass of a nucleus, and the sum of the mass of the neutrons and protons that make up the nucleus. Once this mass difference (also called the mass defect) is known, Einstein's formula (E = mc²) can then be used to compute the binding energy of any nucleus.

The energy given off during either nuclear fusion or nuclear fission is the difference between the binding energies of the fuel and the fusion or fission products.

Binding energy of a deuteron ²H

A deuteron is the nucleus of a deuterium atom, and consists of one proton and one neutron. The masses of the constituents are:

m_proton = 1.007276 u (u is Atomic mass unit)

m_neutron= 1.008665 u

m_proton + m_neutron = 1.007276 + 1.008665 = 2.015941 u

The mass of the deuteron is:

Atomic mass ²H = 2.013553 u

The mass difference = 2.015941 - 2.013553 = .002388 u, and conversion between rest mass and energy is 931.494MeV/u, so a deuteron's binding energy is

0.002388 × 931.494 MeV/u = 2.224 MeV

Thus, expressed in another way, the binding energy is 0.1 % of the total energy corresponding to the mass, hence 90 TJ/kg.

Nuclear binding energy curve

The series of light elements from hydrogen up to sodium have increasing binding energy per nucleon as the atomic mass increases, a region of stability (saturation) occurs from magnesium through xenon, and then binding energy per nucleon decreases as the atomic mass increases. Iron is the most stable and tightly bound element. Fusion produces energy by combining lighter elements into a more stable tighter bound element such as hydrogen into helium, and fission produces energy by splitting heavier elements such as uranium or plutonium into more tightly bound stable elements.

See also

• Chemical bond
• Nuclear fission
• Nuclear fusion
• Nuclear reaction
• Strong nuclear force