THE WAVE-MECHANICAL MODEL
In the 1920's, a more mathematical model of the atom was developed through the work of such
men as deBroglie, Heisenberg, and Schroedinger. Their work in quantum mechanics described
a probability picture of where the electrons at each energy level might best be found. This
region of greatest probability is sometimes referred to as an electron cloud. Unlike the
previous model, the wave-mechanical model does not attempt to explain the path an electron
travels. DeBroglie attributed wave properties to the electron, and these were confirmed later by
experimentation.
Quantum Numbers
Each electron orbital of the atom may be described by a set of four quantum numbers in this
model. They give the position with respect to the nucleus, the shape of the orbital, its spatial
orientation, and the spin of the electron in the orbital.
Principal quantum number
1, 2, 3, 4, 5, etc.
Refers to average distance of the orbital from the
nucleus. 1 is closest to the nucleus and has the
least energy. These numbers correspond to the
shells in the previous model. They are called
energy levels.
Secondary or azimuthal
quantum number
s, p, d, f
(in order of energy)
Refers to the shape of the orbital. The number of
possible shapes is limited by the principal
quantum number. The first energy level has only
one possible shape, the s orbital. The second has
two possible, the s and p orbitals.
.
Magnetic quantum number
s = 1 space-oriented orbital
p = 3 space-oriented orbitals
d = 5 space-oriented orbitals
f = 7 space-oriented orbitals
Spin quantum number
+ spin -spin
The s-orbital shape, is a sphere. The p orbitals
have dumbbell shapes with three possible
orientations. The number of spatial orientations of
orbitals is referred to as the magnetic quantum
number.
Electrons are assigned one more quantum number,
called the spin quantum number. This describes
the spin in either of two possible directions. Each
orbital can be filled by only two electrons, each
with an opposite spin. This is referred to as the
Pauli Exclusion Principle. Therefore each orbital
can hold only two electrons.
It is important to remember that, when there is more than one orbital at a particular energy
level, such as three p orbitals or five d orbitals, only one electron will fill each orbital until
each has one electron. After this, pairing will occur with the addition of one more electron to
each orbital. This is called Hund's Rule of Maximum