UNIT 25 Pauli Exclusion Principle

Although we do not need to go into all the details here, there are certain rules which are useful when considering situations in which there is more than one electron present in an atom. For a start, no two electrons can be associated with the same atomic nucleus and have precisely the same values for all four of the quantum numbers. This is known as the Pauli Exclusion Principle (after Wolfgang Pauli), and it is a particularly potent factor when two similar atoms lie sufficiently close to one another. Regarding the actual shapes of the orbitals, the s types all have spherical symmetry, whereas the p types show elongation along an axis. When all the p orbitals are fully occupied by their permitted complement of electrons, however, these collectively also display spherical symmetry. This is particularly noticeable in the noble gas atoms, which indeed possess only such full shells. Another important property of electron orbitals is that a linear combination of different possible wave functions is also a possible solution of the time-independent Schrodinger equation.

We can now proceed to discuss what happens when two atoms approach each other. It is clear that they must exert a force upon each other, and a moment's reflection reveals that these forces may be either attractive or repulsive. This conclusion comes from the dual facts that matter does not spontaneously explode or implode. In other words, one meets with resistance if an attempt is made to squeeze a piece of condensed matter (i.e. a solid or a liquid) into a smaller volume. Likewise, resistance is encountered if one tries to stretch a piece of material beyond its quiescent dimensions. This indicates that the interatomic potential is repulsive at sufficiently short range and attractive at sufficiently long range, and the implication is thus that there must be an intermediate distance at which there is neither repulsion nor attraction. This will correspond to an interatomic separation for which the forces are precisely balanced, and it is this characteristic distance that essentially determines the density of a piece of material.