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By Jack Barrett

Barrett J. Atomic constitution and periodicity (Royal Society of Chemistry, 2002)(ISBN 0854046577)

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Level one ( M = I ) is singly degenerate (i. e. non-degenerate), level two (IT = 2) has a degeneracy of four, and so on. e. 7. 23). 4 Spatial Orientations of Atomic Orbitals The spatial orientations of the atomic orbitals of the hydrogen atom are very important in the consideration of the interaction of orbitals of different atoms in the production of chemical bonds. The solutions of the Schrodinger wave equation for the hydrogen atom may be represented by the equation: where w is the wave function for an atomic orbital of the hydrogen atom, R represents the radial function (the manner in which v varies along unj' line radiating from the nucleus) and A is the angular function which takes into account variations of y~ dependent upon the particular direction of a line radiating from the nucleus with respect to the coordinate axes.

Such arrangements and their chemical consequences are the subject of this chapter, leading to a general description of the structure of the modern periodic classification of the elements: the Periodic Table. 1 Polyelectronic Atoms ~ The treatment of atoms with more than one electron - polyelectronic atoms - requires consideration of the effects of interelectronic repulsion, orbital penetration towards the nucleus, nuclear shielding, and an extra quantum number - the spin quantum number - which specifies the intrinsic energy of the electron in any orbital.

The permitted values are: m, = +I, +I - 1 , ... 0, ... -(I - l), -1 Atomic Orbitals For instance, a value of I = 2 would yield five different values of in,: 2, I , 0, - 1 and --2. In general there are 21 + 1 values of in, for any given value of 1. In the absence of an externally applied magnetic field, the orbitals possessing a given I value would have identical energies. Orbitals of identical energy are described as being degenerate. In the presence of a magnetic field the degeneracy of the orbitals breaks down; they have different energies.

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