Page 100 - Electrical Properties of Materials

82 Bonds

boxes, or concentric spheres, or rows of seats in the House of Commons filling
up slowly with MPs. The essential thing is that we do form some kind of picture
of the energy shells. And once the shell picture is accepted, it helps us find an
explanation for the next problem, the bond between the atoms.
So you should not be unduly surprised that many alternative explanations
are possible. They reflect attempts to develop intuition in a discipline where
intuition does not come in a natural way.
Whenever confronted with new problems, one selects from this store of
physical pictures the ones likely to be applicable. If one of the physical pictures
does turn out to be applicable, it is a triumph both for the picture and for the
person who applied it. If all attempts fail, then either a new physical picture or
a brighter person is needed to tackle the problem.

5.7 An analogy
One of the most important conclusions of the foregoing discussion was that
‘whenever there is coupling, the energy levels split’. This is a very import-
ant relationship in quantum mechanics, but it could also be regarded as a
simple mathematical consequence of the mathematical formulation. If we have
coupled differential equations, something will always get split somewhere. The
example we are all familiar with is that of coupled electric resonant circuits
shown in Fig. 5.9. If the two circuits are far away from each other, that is they
are uncoupled, both of them have resonant frequencies ω 0 . When the circuits
are coupled, there are two resonant frequencies ω 0 ± a, that is, we may say the
resonant frequencies are split.
Response

Fig. 5.9 M
The coupled circuit analogy. Two
resonant circuits tuned to ω 0 when far
apart (no coupling between them),
have their resonant frequency split to
0
ω 0 ± a (cf. E 0 ± A) when coupled. ω – a ω 0 ω + a Frequency
0

Exercises
5.1. Discuss qualitatively the various mechanisms of bond- 5.3. The interaction energy between two atoms may be phe-
ing. Give examples of materials for each type of bond and nomenologically described by eqn (5.8). Show that the mo-
also materials that do not have a clear single bond type. lecule will break up when the atoms are pulled apart to a
distance
5.2. Show that the force between two aligned permanent
–4
dipoles, a distance r apart, is attractive and varies as r .
1/(n–m)
r r b = n +1 r 0 ,
≺————–
+– +– m +1
˙ d ˙ d
↔ ↔