bei48482_FM

The Solid State 357

Thus the 3sband in solid sodium is only half filled by electrons (Fig. 10.22) and the

Fermi energy Flies in the middle of the band.

When a potential difference is applied across a piece of solid sodium, 3selectrons

can pick up additional energy while remaining in their original band. The additional

energy is in the form of KE, and the drift of the electrons constitutes an electric current.

Sodium is therefore a good conductor, as are other solids with partly filled energy bands.

Magnesium atoms have filled 3sshells. If the 3slevel simply spreads into a 3sband

in solid magnesium, as in Fig. 10.21b, there would be a forbidden band above it and

the 3selectrons could not easily pick up enough energy to jump the forbidden band

to the empty band above it. Nevertheless magnesium is a metal. What actually happens

is that the 3pand 3sbands overlap as magnesium atoms become close together to give

the structure shown in Fig. 10.21a. Ap(l1) atomic level can hold 2(2l1) 

2(2 1) 6 electrons, so a pband formed by Natoms can hold 6Nelectrons. Together

Figure 10.20The energy levels of sodium atoms become bands as their internuclear distance decreases.

The observed internuclear distance in solid sodium is 0.367 nm.

Figure 10.22The 3senergy band

in solid sodium is half filled with

electrons. The Fermi energy Fis

in the middle of the band.

Overlapping

energy bands

Forbidden

band

(b)

(a)

Figure 10.21(a) The energy bands

in some solids may overlap to give

a continuous band. (b) A forbidden

band separate nonover-lapping en-

ergy bands in other solids.

Solid sodium

3 s

2 p

2 s

1 s

Internuclear distance, nm

0 0.3670.5 1.0 1.5

− 30

− 20

− 10

0

Energy, ev

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