Page 295 - Electrical Properties of Materials

Microscopic theory (quantum-mechanical) 277

(a) 1s 2s 2p
B

C

N

(b)
s 1 s 2 2 p s 3 3 p 3 d s 4
Cr

Mn

Fe

Co

Ni

Fig. 11.16
The electron configurations of (a) boron, carbon, and nitrogen and (b) chromium, manganese, iron, cobalt, and nickel.

The consequences of (2) are even more important. It follows from there that
states with identical spins are occupied first. Thus, boron with a configuration
2
1
2
1s 2s 2p has one electron with spin ‘up’ in the outer shell [see Fig. 11.16(a)];
carbon has two electrons with spin up, and nitrogen has three. Similarly all five
electrons of chromium and manganese in the 3d shell have spins up, and the
states with opposite spins start to fill up only later, when there is no alternative.
This is shown in Fig. 11.16(b), where the electronic configurations are given
for chromium, manganese, iron, cobalt, and nickel.
We shall return to the spins of the 3d electrons a little later; first let me sum-
marize the main points of the argument. The most important thing to realize
is that electrons in an atom do not act individually. We have no right to as-
sume (as we did in the classical treatment) that all the tiny electronic currents
are randomly oriented. They are not. They must obey Pauli’s principle, and so
within an atom they all occupy different states that do bear some strict rela-
tionships to each other. The resultant angular momentum of the atom may be
obtained by combining the properties of the individual electrons, leading to the
quantum number J, which may also be zero. Thus an atom that contains many
‘magnetic’ electrons may end up without any magnetic moment at all.
You may ask at this stage what is the evidence for these rather strange tenets
of quantum theory? Are the magnetic moments of the atoms really quantized?
Yes, they are. The experimental proof actually existed well before the theory
was properly formulated.