|MadSci Network: Physics|
It is not exactly true that a shell must be complete before the next shell starts to form in an atom. The reason is that the energy of an electron depends both on the shell and on a quantity called "angular momentum". Electrons with low angular momentum in a shell tend to be closer to the nucleus and have lower energies than electrons with high angular momentum in the same shell. This happens because an electron that tends to be far from the nucleus feels more strongly the repulsive force of the electrons that are closer to the nucleus and this "pumps up" its energy, so to speak. Like energy, angular momentum in an atom can take only discrete values. Angular momentum values can be labeled with a number l, which takes integer values starting with 0, and increases with increasing angular momentum. Electrons with l=0 are called "s" electrons, electrons with l=1 are called "p" electrons, with l=2, 3, 4, 5, ... are called "d", "f", "g", "h" ... electrons. As we add electrons to an atom, they take the shell and the angular momentum that gives them the lowest energy. According to the Pauli exclusion principle, in any given shell there can be up to 2*(2*l+1) (that's two times l+l+1) electrons in a shell with the same l value. Therefore we can have only 2 s electrons, 6 p electrons, 10 d electrons, and so forth until the shell is complete. Within the SAME shell s electrons have lower energy than p electrons, and p electrons have lower energy than d electrons and so on as we explained above. Thus s electrons start to fill the M shell and d electrons complete the shell, but how do energies of those d electrons compare to the energy of the s electrons of the NEXT shell? It so happens that the d electrons of the M shell can have slightly higher energies than the s electrons of the N shell. Actually their energies depend on how many electrons the atom has, therefore the available places in the M shell compete with the N shell for the lowest energy to offer to the electrons. An authoritative book on the subject, "The Theory of Atomic Structure and Spectra" by Robert D. Cowan, p. 115, says that this fact can only be demonstrated quantitatively with a complex calculation, and only in some cases. Calculations of many-electron structures are very difficult and its accuracy is very limited. What happens in reality can be deduced from experiment though. Table 4-3 of that book shows that the N shell starts to fill with s electrons in potassium when the M shell only has 2 s electrons and 6 p electrons. The missing d electrons of the M shell start to appear in scandium. As we add electrons, it can happen that the M shell can gain or loose an extra electron from the N shell. This happens for example when we go from vanadium to chromium and manganese or when we go from nickel to cooper and zinc. The same happens when the O shell starts to form before the N shell is complete in rubidium. This situation only happens with neutral and singly ionized (i.e. those with an electron missing) atoms. More ionized atoms (those missing two or more electrons) don't show this behavior because the energies of their electrons don't depend so strongly on angular momentum. Vladimir Escalante
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