18.3.4 Binding Energy per Nucleon

Besides the binding energy BE, another important parameter for a nuclide is the binding energy per nucleon BE/A. As the name suggests, BE/A is simply the BE of a nuclide divided by the number of nucleons A in that nuclide. While BE represents the energy required to separate all the nucleons, BE/A roughly represents the energy to remove one nucleon from the nucleus. Since a nuclear transmutation occurs as long as one nucleon is separated from the nucleus, BE/A is a better indicator of the stability of a nuclide than BE. (Kind of like the GDP per capital is a better indicator of a country’s affluence level than the GDP).

NuclideABE (MeV)BE/A (MeV)
Deuterium-222.231.12
Helium-4428.297.07
Lithium-7740.155.74
Beryllium-9958.136.46
Iron-5656492.248.79
Lead-2062061622.277.88
Polonium-2102101645.167.83
Uranium-2352351783.807.59
Uranium-2382381801.637.57

An interesting trend presents itself when BE/A is plotted against A.

Note that:

  • The general trend is that BE/A increases with A for small nuclei (A<56) but decreases with A for large nuclei (A>56).[1]
  • Iron-56, with the highest BE/A of 8.8 MeV, is recognized as the most strongly bound and most stable nuclide in the world.
  • When small nuclei undergo fusion, the product nuclei tend to have higher BE/A than the reactant nuclei. A good example is the deuterium-tritium fusion.

\displaystyle \displaystyle {}_{1}^{2}H+{}_{1}^{3}H\to {}_{2}^{4}He+{}_{0}^{1}n

  • Conversely, when large nuclei undergo fission, the product nuclei tend to have higher BE/A than the reactant nuclei. A good example is the uranium fission.

\displaystyle \displaystyle {}_{0}^{1}n+{}_{{92}}^{{235}}U\to {}_{{56}}^{{141}}Ba+{}_{{36}}^{{92}}Kr+3{}_{0}^{1}n

  • Since the number of nucleons remain the same in a nuclear reaction, a higher BE/A also implies higher total BE. This explains why energy is released by the fusion of small nuclei (e.g. hydrogen), and the fission of large nuclei (e.g. uranium).

Concept Test

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[1] If you’re interested to know the reason behind this trend, and why He-4 and O-16 are outliers, see Appendix B:Nuclear Force and Appendix C:Magic Numbers.

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