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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.

1 The 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.

2 The 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. IronThis article is about metallic iron. For the ironing device, see ironing manganese iron cobalt Fe Ru Full table General Name, Symbol, Number iron, Fe, 26 Chemical series transition metal Group, Period, Block 8 (VIIIB), 4 , d Density, Hardness 7874 kg/m3, 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 HeliumHelium is a colorless, odorless, tasteless chemical element, one of the noble gases of the periodic table of elements. Its boiling and melting points are the lowest among the elements; except in extreme conditions, it exists only as a gas. The second most, and fission produces energy by splitting heavier elements such as UraniumUranium is a chemical element in the periodic table that has the symbol U and atomic number 92. A heavy, silvery-white, toxic, metallic , and naturally- radioactive element, uranium belongs to the actinide series and its isotope uranium-235 is used as the or PlutoniumPlutonium is a radioactive, metallic, chemical element. It has the symbol Pu and the atomic number 94. Its atomic weight is 244. 06, its density 19,800 kg/m3. It is the element used in most modern nuclear weapons. The most important isotope of plutonium i into more tightly bound stable elements.