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Physical chemistry 290

This gives a density of states diagram which has the form shown in Fig. 2. The equation
may also be modified to calculate the maximum energy of the electrons from their
3
number density, in the solid. As a is the volume of the box, the number density of the
3
electrons, ρ, is equal to N/a , and E max is given by:

The free electron model is remarkably accurate in calculations of electron energies in
simple metals. The major difference between the free electron model and the tightly
bound electron model is that in the free electron model the band is open-ended, and does
not have an upper energy limit. More accurate approaches to band theory account for
both the highly delocalized nature of the electrons, and the regular array of nuclear
potentials.

Fig. 2. Density of states diagram
resulting from the free electron model.

Electrons in bands

As with molecular orbitals, the energy levels in a band are progressively filled from the
lowest energy upwards. At zero Kelvin, the electrons occupy only the lowest energy
levels available. The highest occupied energy level is referred to as the Fermi energy or