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).

Nuclide	A	BE (MeV)	BE/A (MeV)
Deuterium-2	2	2.23	1.12
Helium-4	4	28.29	7.07
Lithium-7	7	40.15	5.74
Beryllium-9	9	58.13	6.46
Iron-56	56	492.24	8.79
Lead-206	206	1622.27	7.88
Polonium-210	210	1645.16	7.83
Uranium-235	235	1783.80	7.59
Uranium-238	238	1801.63	7.57

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.

• 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.

• 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).

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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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