bei48482_FM

An electron in a solid can only have energies that fall within its energy bands. The

various outer energy bands in a solid may overlap, as in Fig. 10.21a, in which case its

valence electrons have available a continuous distribution of permitted energies. In

other solids the bands may not overlap, as in Fig. 10.21b, and the intervals between

them represent energies their electrons cannot have. Such intervals are called forbidden

bandsor band gaps.

Figure 9.11 shows the distribution of electron energies in a band at various tem-

peratures. At 0 K all levels in the band are filled by electrons up to the Fermi energy

F, and those above Fare empty. At temperatures above 0 K, electrons with energies

below Fcan move into higher states, in which case Frepresents a level with a 50 per-

cent likelihood of being occupied.

A sodium atom has a single 3svalence electron. Each s(l0) atomic level can

hold 2(2l1)2 electrons, so each sband formed by Natoms can hold 2Nelectrons.

356 Chapter Ten

Internuclear distance

Energy

(b)

Internuclear distance

Energy

(c)

Internuclear distance

Energy

(a)

Figure 10.19The 3slevel is the highest occupied level in a ground-state sodium atom. (a) When two

sodium atoms come close together, their 3slevels, initially equal, become two separate levels because

of the overlap of the corresponding electron wave functions. (b) The number of new levels equals the

number of interacting atoms, here 5. (c) When the number of interacting atoms is very large, as in

solid sodium, the result is an energy band of very closely spaced levels.

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