Page 294 - Electrical Properties of Materials

276 Magnetic materials

4. Energy levels split in the presence of a magnetic field. The splitting is pro-
∗
∗ Discovered well before the advent of portional to the magnetic field. This is known as the Zeeman effect. In
quantum mechanics. Pieter Zeeman re- quantum-mechanical terms this means that the energy of a magnetic dipole
ceived the Nobel Prize for it in 1902.
in a magnetic field H (taken in the z-direction) may be written as
H
The term –e /2m is called a Bohr E mag =–(μ m ) z μ 0 H =–ge z μ 0 . (11.36)
2m
magneton and denoted by μ mB .
We may rewrite eqn (11.36) in the form,

H
E mag = gμ mB z μ 0 , (11.37)

where z / , as we have seen before, may take the values j, j –1, etc.
down to –j.

We now know everything about the magnetic properties of an electron in
the various states of the hydrogen atom. In general, of course, the hydrogen
atom is in its ground state, for which l = 0 and m l = 0, so that only the spin of
1
the electron counts. The new quantum number j comes to , and the possible
2
values of the angular momentum in any given direction are /2 and – /2.
Furthermore, g = 2, and the magnetic moment is
The magnetic moment of hydro- μ m = μ mB . (11.38)
gen happens to be one Bohr mag-
neton. We can get the magnetic properties of more complicated atoms by com-
bining the quantum numbers of the individual electrons. There exists a set of
rules (known as Hund’s rules) that tell us how to combine the spin and orbital
quantum numbers in order to get the resultant quantum number J. The role of
J for an atom is exactly the same as that of j for an electron. Thus, for example,
the total angular momentum is given by

= {J(J +1)} 1/2 , (11.39)

and the possible components of the angular momentum vector along any
axis by

J, (J –1), ... , (–J +1), – J.

The general rules are fairly complicated and can be found in textbooks on
magnetism. I should just like to note two specific features of the magnetic
properties of atoms:
1. Atoms with filled shells have no magnetic moments (this is because the
various electronic contributions cancel each other);
2. The spins arrange themselves so as to give the maximum possible value
consistent with the Pauli principle.
It follows from (1) that helium and neon have no magnetic moments; and
stretching the imagination a little one may also conclude that hydrogen, lith-
ium, and silver, for example, possess identical magnetic properties (because all
of them have one outer electron).