The Relationship between Nuclear Stability and the Neutron-to-Proton Ratio

In a previous article on the weak force and beta decays, I have used but not really explained the concept of stable isotopes. I think this deserve a separate article in order to be more clear about what kind of stability we are talking about.

In this plot of the number of protons (vertical axis, Z) versus the number of neutrons (horizontal axis, N), each black point with (Z <= 83) corresponds to a stable nucleus:
islandOfStability (The image is from NewScientist it’s not in my intention to make money with it, I only use it in order to improve my understanding of the topic.) In this classification, a stable nucleus is arbitrarily defined as one with a half-life (i.e. the time required for half of the initial number of atoms present in a sample to decay in a first-order reaction) longer than 46 billion years (10 times the age of Earth). As the number of protons (the atomic number) increases, the number of neutrons required for a stable nucleus increases even more rapidly. Isotopes shown in blue towards the green, yellow and cyan are progressively less stable and more radioactive; the farther an isotope is from the diagonal band of stable isotopes, the shorter its half-life. Data source: NewScientist

NOTES:
(1) The heaviest nuclei in nature, uranium 238U, are unstable, but having a lifetime of 4.5 billion years, close to the age of the Earth, they are still relatively abundant; they (and other nuclei heavier than iron) may have formed in a supernova explosion preceding the formation of the solar system

(2) Several stable isotopes of light atoms have a neutron-to-proton ratio equal to 1 Z=N for e.g. 2-2-He, 40-20-Ca. After the calcium isotope (Z > 20), all other stable nuclei have a higher neutron-to-proton ratio (N > Z), which increases steadily to about 1.5 for the heaviest nuclei. Regardless of the number of neutrons, however, all elements with Z > 83 are unstable and radioactive

(3) News of superheavy elements arrive almost everyday. Evidence for the artificial creation of element 117 has recently been obtained at an accelerator laboratory located in Germany. Superheavy elements in this so-called island of stability could act as powerful nuclear fuel for future fission-propelled space missions. They might also be exhibit useful new chemical properties. Element 114, for example, has shown hints that it behaves like a gas at room temperature even though it should be a member of the lead family on the periodic table

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