Isobar (nuclide)
Isobars are atoms (nuclides) of different chemical elements that have the same number of nucleons. Correspondingly, isobars differ in atomic number (or number of protons) but have the same mass number. An example of a series of isobars would be 40S, 40Cl, 40Ar, 40K, and 40Ca. The nuclei of these nuclides all contain 40 nucleons; however, they contain varying numbers of protons and neutrons.
The term "isobars" (originally "isobares") for nuclides was suggested by Alfred Walter Stewart in 1918. It is derived from the Greek word isos, meaning "equal" and baros, meaning "weight".
The same mass number implies neither the same mass of nuclei, nor equal atomic masses of corresponding nuclides. From the Weizsäcker's formula for the mass of a nucleus
where mass number A equals to the sum of atomic number Z and number of neutrons N, and mp, mn, aV, aS, aC, aA are constants, one can see that the mass depends on Z and N non-linearly, even for a constant mass number. For odd A, it is admitted that δ = 0 and the mass dependence on Z is convex (or on N or N − Z, it does not matter for a constant A). This explains that beta-decay is energetically favorable for neutron-rich nuclides, and positron decay is favorable for strongly neutron-deficient nuclides. Both decay modes do not change the mass number, hence an original nucleus and its daughter nucleus are isobars. In both aforementioned cases, a heavier nucleus decays to its lighter isobar.
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