de Broglie's concept afforded scientists a new way of viewing the electron.

New experiments provided new insights. The Stern-Gerlach [local] experiment suggested that electrons possessed an intrinsic property called electron spin. When atomic sprectra were studied under conditions where the excited atoms were in a strong magnetic field, lines in the spectra split forming multiplets (doublets, triplets, etc.) This was called the Zeeman effect [local]..

Erwin Schrodinger [local] developed an equation that calculated energies of electrons on the basis of "wave mechanics." P.A.M. Dirac added to Schrodinger's work by including information that explained the magnetic and spin aspects of the electron. Schrodinger and Dirac shared the Nobel Prize in physics in 1933 "for the discovery of new productive forms of atomic theory."

Schrodinger's equation in abstract form :

The operator is a set of mathematical instructions. The wave function is a function of the coordinates (x,y,z) of the position of the electron. E is the sum of the potential energy due to the attraction of the electron for the nucleus and the kinetic energy of the electron.

This equation thus had many solutions. Each solution consisted of a wave function that was characterized by a particular energy. A specific wave function is termed an orbital.

It turns out that the square of the wave function tells the probability of finding that electron near that point in space. This probability can be represented by a probability distribution which gives a sort of electron density map for where around the nucleus the electrons are most probably located at any instant in time. Usually small dots of gray or color are used to show this. When pictures of orbitals are presented they are really these electron density maps.

A radial probability distribution shows the probability of finding an electron for an orbital at some distance from the nucleus. Radial probability distributions are shown as an x-y graph with distance from the nucleus on the x-axis and the radial probability on the y-axis. The peak represents highly probable distances.

The points where the line approaches the x-axis are termed nodes. In three dimensional distribution, these are nodal surfaces.

The visualization and presentation of the probability distribution of orbitals is becoming better with the advent of desktop computers.

This site allows you to select the orbital and see the spatial distribution.

Orbitals can be viewed using the Chime plugin from MDL that permits 3-D manipulation.

Manthey has created a very complete set of orbitals, [local] be sure to read the information about the table and select different views. This table allows you to see more orbitals than most sites including g and h orbitals.