What is NZ Graph? | Maximizing Binding Energy

For a Nucleus of mass number A, what is be the correct ratio of neutrons and protons? Can ''any'' combination of neutrons and protons create a stable nucleus?
The answer to that Question leads to the NZ Graph, or the NZ Curve. It is found that for all the stable nuclei found in nature, its neutron to proton ratio fall on a curve, also known as the Stability Curve, surrounded by regions of unstability. There are two distinct observations associated with such a curve:
1) For small mass number, the NZ Curve (or the Stability Curve) coincides with the N=Z line, i.e. number of neutrons is equal to the number of protons.
2) For increasing mass number, the NZ Curve slightly deviates from the N=Z line, as the number of neutrons starts progressively increasing compared to the number of protons.
Two conclusions can be drawn from these observations :
A) Neutrons and Protons arrange themselves in energy levels. Because of this reason, an equal number of neutrons and protons lead to the minimum energy configuration of the nucleus. When there is an excess number of either neutrons or protons, then the overall energy of the nuclear configuration increases leading to an instability on the nucleus. Such nuclear configurations will tend to undergo beta decay reactions and 'equalize' their number of neutrons and protons.
B) With increasing mass number the number of neutrons slightly increases to increase the overall nuclear force that holds the nucleus together and compensate for the ever increasing coulombic repulsion. This is because nuclear forces are short range forces, while coulombic repulsion is a long range force. For large nuclei, short range nuclear forces are not sufficient enough, and you need ever increasing number of neutrons to maintain a stable nucleus.
As you can see, the NZ Graph tells us the optimum ratio of neutrons and protons for any given nucleus of fixed mass number.
There is also a way of obtaining a theoretical approximation for the NZ Curve. This is by Maximizing the Binding Energy Expression, which I discuss in the video.

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15) Nature of (Strong) Nuclear Force) ►    • Nature of (Strong) Nuclear Force  
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