Page 76 - Electrical Properties of Materials

The periodic table 59
l = 0 1 2 3 4 5 6 7
s p d f g h i k

Thus, if you wish to refer to the states with n = 3 and l = 1, you call them the
3p states or the 3p configuration. The reason for this rather illogical notation
is of course historical. In the old days when only spectroscopic information
was available about these energy levels they were called s for sharp, p for
principal, d for diffuse, and f for fundamental. When more energy levels were
found, it was decided to introduce some semblance of order and denote them
by subsequent letters of the alphabet. That is how the next levels came to bear
the letters g, h, i, k, etc.

4.3 Electron spin and Pauli’s exclusion principle

The quantum numbers n, l, and m l have been obtained from the solution of
Schrödinger’s equation. Unfortunately, as I mentioned before, they do not rep-
resent the whole truth; there is one more quantum number to be taken into
account. It is called the spin quantum number, denoted by s, and it takes the
1
values ± .
2
Historically, spin had to be introduced to account for certain spectroscopic
measurements, where two closely spaced energy levels were observed when
only one was expected. These were explained in 1925 by Uhlenbeck and
Goudsmit by assuming that the electron can spin about its own axis. This clas-
sical description is very much out of fashion nowadays, but the name spin stuck
and has been universally used ever since. Today the spin is looked upon just
as another quantum number obtainable from a more complicated theory which
includes relativistic effects as well.
So we have now four quantum numbers: n, l, m l , and s. Any permissible
combination of these quantum numbers [eqn (4.28) shows what is permissible]
gives a state; the wave function is determined, the electron’s energy is deter-
mined, everything is determined. But what happens when we have more than
one electron? How many of them can occupy the same state? One, said Pauli.
There can be no more than one electron in any given state.ThisisPauli’s Wolfgang Pauli, Nobel Prize,
exclusion principle. We shall use it as a separate assumption, though it can be 1945.
derived from a relativistic quantum theory, due to Dirac.
Paul Adrien Maurice Dirac, Nobel
Although both the spin and the exclusion principle are products of rather
Prize, 1933.
involved theories, both of them can be explained in simple terms. So even if
you do not learn where they come from, you can easily remember them.

4.4 The periodic table
We have so far tackled the simplest configuration when there are only two
particles: one electron and one proton. How should we attempt the solution for
a more complicated case; for helium, for example, which has two protons and
two electrons? (Helium has two neutrons as well, but since they are neutral
they have no effect on the electrons; thus when discussing the energy levels of
electrons neutrons can be disregarded.)
The answer is still contained in Schrödinger’s equation, but the form of
the equation is more complicated. The differential operator ∇ operated on the