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in the MOs are, nonetheless, constantly moving. Although the electrons are described in terms of quantum mechanical wavefunctions, the electrons have kinetic energy. Therefore, it is possible to calculate an electron velocity. The electrons in some MOs can be thought of as moving to the right. There are corresponding MOs of identical energy with electrons moving to the left. With all of the MOs filled, as shown in Figure 19.3, there will be no net electron current because there are an equal number of electrons moving to the right and to the left. In three dimensions, for any direction you pick, there will be equal probability of electrons moving in that direction and in the exact opposite direction.

However, when the metal rod in Figure 19.1 is connected to a battery, things change. One end of the rod is connected to the positive side of the battery and the other end is connected to the negative end of the battery. The connection to the battery changes what the electrons feel. Without the battery, the electrons feel the positive charges of the sodium nuclei and the negative charges of other electrons. Any one electron in the middle of the rod sees no difference between right and left. But with the battery there is an additional influence, the electric field produced across the metal rod by the battery. The electrons are attracted to the positive end and repelled from the negative end. The effect is to modify the system with the result that some electrons are in levels above the Fermi level that existed without the battery (see Figure 19.4). The electron states of the system are changed such that there are more electrons moving in the direction toward the positive end of the metal rod than toward the negative end.

FIGURE 19.4. Schematic of the sodium metal 3s band of levels as shown in Figure 19.3, but now with the influence of being connected to the battery. The effect is to put some electrons above the no battery Fermi level, taking them from filled MOs to empty MOs. These electrons are represented by the arrows above the Fermi level.

Quantum theory shows that it is necessary to have electrons above the Fermi level for electron conduction to occur. Because there are only infinitesimal differences in energy between the levels, even a very low voltage applied to the rod, which produces a tiny electric field, is sufficient to put some electrons above the Fermi level. The result is an electrical current flowing throw the metal rod. Electrons leave the positive end of the rod and are replaced by electrons entering from the negative end. For a bigger electric field (higher voltage), more electrons will be above the zero field Fermi level, and the electrical current is bigger. The detailed quantum theory of electrical conductivity in metals says that current will flow when an electric field is applied even at absolute zero temperature. Heat is not required for a metal to conduct. We will see below that this is not the case for semiconductors, and also, that heat, which is present at all temperatures above 0° K, actually interferes with electrical conductivity in metals.

INSULATORS

Insulators Do Not Conduct Electricity Because the Band Is Filled

Metals conduct electricity easily even at 0° K because the electrons only fill part of the band of states, as shown in Figure 19.3 and 19.4. A very small electric field (voltage) will put electrons above the Fermi level. An insulator is a material, such as glass or plastic, that does not conduct electricity at any temperature. A schematic illustration of the band structure of an insulator is shown in Figure 19.5. In sodium metal, the 3s electrons are the valence electrons. The valence band is only half filled. In an insulator, like quartz (SiO2, silicon dioxide), which is very similar to glass, sharing of the electrons completes the shell of electrons. The interactions in a quartz crystal produce a band of states, with delocalized MOs, like in a metal. However, the valence band is completely filled. There are two electrons in each MO because there are N MOs but 2N