Nuclear properties

By definition, any two atoms with an identical number of protons in their nuclei belong to the same chemical element. Atoms with equal numbers of protons but a different number of neutrons are different isotopes of the same element. For example, all hydrogen atoms admit exactly one proton, but isotopes exist with no neutrons hydrogen-1, one neutron (deuterium), two neutrons (tritium) and more than two neutrons. The hydrogen-1 is by far the most common form, and is sometimes called protium.^[66] The known elements form a set of atomic numbers from hydrogen with a single proton up to the 118-proton element ununoctium.^[67] All known isotopes of elements with atomic numbers greater than 82 are radioactive.^[68][69]

About 339 nuclides occur naturally on Earth,^[70] of which 256 (about 76%) have not been observed to decay, and are referred to as "stable isotopes". For 80 of the chemical elements, there is at least one stable isotope. Elements 43, 61, and all elements numbered 83 or higher have no stable isotopes. As a rule, there is, for each element, only a handful of stable isotopes, the average being 3.1 stable isotopes per element which has any stable isotopes. Twenty-seven elements have only a single stable isotope, while the largest number of stable isotopes observed for any element is ten, for the element tin.^[71]

Stability of isotopes is affected by the ratio of protons to neutrons, and also by presence of certain "magic numbers" of neutrons or protons which represent closed and filled quantum shells. These quantum shells correspond to a set of energy levels within the shell model of the nucleus; filled shells, such as the filled shell of 50 protons for tin, confers unusual stability on the nuclide. Of the 256 known stable nuclides, only four have both an odd number of protons and odd number of neutrons: hydrogen-2 (deuterium), lithium-6, boron-10 and nitrogen-14. Also, only four naturally occurring, radioactive odd-odd nuclides have a half-life over a billion years: potassium-40, vanadium-50, lanthanum-138 and tantalum-180m. Most odd-odd nuclei are highly unstable with respect to beta decay, because the decay products are even-even, and are therefore more strongly bound, due to nuclear pairing effects