A
new and better quantum theory was developed in the 1920's by an
Austrian and a German physicist, Erwin Schrodinger and Werner Heisenberg.
Their wave mechanics is mathematically intimidating, and
almost seems to view the world as a set of solutions of differential
equations. It succeeded in explaining the structure of multielectron
atoms, the structure of the Periodic table, and the theory of bonding
between atoms in molecules  impressive accomplishments for any
theory. The picture of atoms and molecules that resulted is essentially
that which we use today. We will make use of the results of wave
mechanics  energy levels and atomic structure  without going through
the mathematics that led to those results.
As in the simpler Bohr theory, the energy of an electron in an atom
is restricted to certain values, or is quantized. Three quantum
numbers instead of one are required to describe an electron, and
they are designated n, l, and m.
The average distance of the electron from the nucleus depends primarily
on n, which is called the principal quantum number.
The geometry of bonding around the atom depends primarily on quantum
number l, called the orbitalshape, or azimuthal,
quantum number. The energy of an electron in an atom is a
function of n and to a lesser degree of l.
The orbitalorientation, or magnetic quantum number, m,
describes how the electron's orbit is oriented in space relative
to some external reference such as a magnetic or electric field.
In the absence of such fields, all m states for a
given n and l value have the same energy.

