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A graphical representation of the semi-empirical binding energy formula. The binding energy per nucleon in MeV (highest numbers in yellow, in excess of 8.5 MeV per nucleon) is plotted for various nuclides as a function of Z, the atomic number (y-axis), vs. N, the number of neutrons (x-axis). The highest numbers are seen for Z = 26 (iron).
The binding energy per nucleon (in MeV) shown as a function of the neutron number N and atomic number Z as given by the semi-empirical mass formula. A dashed line is included to show nuclides that have been discovered by experiment.
[5] [6] Nuclear binding energy derives from the nuclear force or residual strong force, which is mediated by three types of mesons. The average nuclear binding energy per nucleon ranges from 1.11226 MeV for hydrogen-2 to 8.7945 MeV for nickel-62. Nuclear level: Quantum chromodynamics binding energy
[4]: 46–50 Normally binding energy is referred to and plotted as average binding energy per nucleon. [9] According to Lilley, "The binding energy of a nucleus B is the energy required to separate it into its constituent neutrons and protons."
For instance, the magic number 8 occurs when the 1s 1/2, 1p 3/2, 1p 1/2 energy levels are filled, as there is a large energy gap between the 1p 1/2 and the next highest 1d 5/2 energy levels. The atomic analog to nuclear magic numbers are those numbers of electrons leading to discontinuities in the ionization energy .
These nuclides lie at the very bottom of the valley of stability. From this bottom, the average binding energy per nucleon slowly decreases with increasing atomic mass number. The heavy nuclide 238 U is not stable, but is slow to decay with a half-life of 4.5 billion years. [1] It has relatively small binding energy per nucleon.
The energy of helium-4 nuclear binding per nucleon is stronger than in any of those elements (see nucleogenesis and binding energy), and thus no energetic "drive" was available to make elements 3, 4, and 5 once helium had been formed.
It is also the isotope with the lowest mass per nucleon, 930.412 MeV/c 2, though not the isotope with the highest nuclear binding energy per nucleon, which is nickel-62. [7] However, because of the details of how nucleosynthesis works, 56 Fe is a more common endpoint of fusion chains inside supernovae, where it is mostly produced as 56 Ni.