Of all the elements known, as listed in the periodic table, only four classes of such polynomials are needed to describe the shape of these orbitals, designated as s, p, d, and f.
The chemistry of the main group elements is dominated primarily by the electronic configuration in just the s and p orbitals; that of the transition metals by the electronic configuration of electrons in the d orbitals; and that of the lanthanides and actinides by the electronic configuration of electrons in the f orbitals. While this is generally true, and is represented in the layout of the periodic table, other factors, such atomic radius, atomic mass, and increased accessibility of additional electronic states also contribute to the chemistry of the elements as atomic size increases.
Progressing through a group from lightest element to heaviest element, the outer-shell electrons (those most readily accessible for participation in chemical reactions) are all in the same type of orbital, with a similar shape, but with increasingly higher energy and average distance from the nucleus. For instance, the outer-shell (or "valence") electrons of the first group, headed by hydrogen all have one electron in an s orbital. In hydrogen, that s orbital is in the lowest possible energy state of any atom, the first-shell orbital (and represented by hydrogen's position in the first period of the table). In francium, the heaviest element of the group, the outer-shell electron is in the seventh-shell orbital, significantly further out on average from the nucleus than those electrons filling all the shells below it in energy. As another example, both carbon and lead have four electrons in their outer shell orbitals.
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