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In most stable isotopes the binding energy per nucleon lies between 7 and 9 MeV. There are two competing forces in the nuclei, electrostatic repulsion between protons and the attractive nuclear force between nucleons (protons and neutrons). The electrostatic force is a long range force that becomes more difficult to compensate for as more protons are added to the nucleus. The nuclear force, which arises as the residual strong force (the strong force binds the quarks together within a nucleon), is a short range force that only operates on a very short distance scale (~ 1.5 fm) as it arises from a Yukawa potential. (Electromagnetism is a long range force as the force carrier, the photon, is massless; the nuclear force is a short range force as the force carrier, the pion, is massive). Therefore, larger nuclei tend to be less stable, and require a larger ratio of neutrons to protons (which contribute to the attractive strong force, but not the long-range electrostatic repulsion). For the low Z nuclides the ratio of neutrons to protons is approximately 1, though it gradually increases to about 1.5 for the higher Z nuclides as shown below on the Nuclear Stability Curve.
In other words to combat the effect of the increase in electrostatic repulsion when the number of protons increases the number of neutrons must increase more rapidly to contribute sufficient energy to bind the nucleus together.
As we noted earlier there are a number of isotopes for each element of the Periodic Table. It has been found that the most stable isotope for each element has a specific number of neutrons in its nucleus. Plotting a graph of the number of protons against the number of neutrons for these stable isotopes generates what is called the Nuclear Stability Curve:
Note that the number of protons equals the number of neutrons for small nuclei. But notice also that the number of neutrons increases more rapidly than the number of protons as the size of the nucleus gets bigger so as to maintain the stability of the nucleus. In other words more neutrons need to be there to contribute to the binding energy used to counteract the electrostatic repulsion between the protons.
