Odd-Even Relationships

We have seen that four nuclides, each having an integral number of a quartets, comprise about 70 percent of the earth s crust. These four obviously have even numbers both of protons and neutrons. Moreover, of the 274 stable nuclides known, 162 likewise have even numbers both of protons and neutrons. Only four (H2, Li6, B10, and N14) have odd numbers both of protons and neutrons, whereas the remaining hundred or so stable nuclides are odd-even nuclei, about half of them having even numbers of neutrons, the other half having even numbers of protons. The differences in the relative abundances of the various classes of nuclides are very striking, and their explanations are a favorite topic for conjecture among nuclear chemists. Many such explanations involve the concept of closed nuclear shells (or a quartets ) with the assumption that complete shells (and possibly half-filled shells also) are especially stable. (See, for example, Exercise 8.) 

A number of additional observations indicate that there is extra stability associated with nuclei having an even number of protons, of neutrons, or, more especially, even numbers of both. Elements of odd atomic number have no more than two stable isotopes. Of these elements, about half exist as one stable nuclide only, and two have no stable forms. Aside from the four exceptions mentioned in the preceding paragraph, each stable nucleus having an odd number of protons must have an even number of neutrons. Among the natural radioactive series, about 20 nuclides of even Z, but only 2 of odd Z, have half-lives of over one day. 

In contrast, the average number of stable isotopes for elements having even atomic numbers below 84 (polonium) is far greater. Tin (Z = 50) has, for example, 10 stable isotopes, and xenon (Z = 54) has 9. All even elements below polonium have at least two stable isotopes except for beryllium. Of the isotopes of a given element of even Z, generally no more than two may have odd numbers of neutrons. The others must be even-even nuclei. 

Note that in the isobaric series above, conversion of one isobar to its neighbor is simply a conversion from an even-odd to an odd-even nuclide or vice versa. 

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