What is the difference between Free Electron Theory and Band Theory of solids?

Answer 1

Free Electron Theory:

This theory tells that, metals conduct electricity because of the presence of free electrons in it. The outermost shells of metal atoms will be loosely bound with their nucleus. So the electrons in it are free to move anywhere in the solid.These electrons are called free electrons and they are responsible for the conduction of electricity.

Band theory of solids:

A solid is assumed to contain many bands in which the electrons in it are packed. The most important are valence band and conduction band. The energy of electrons in these bands will be different.The difference in energies of valence band and conduction band determines whether the solid is a conductor, semi - conductor or insulator.For insulators, the difference between energies of them ( energy gap ) will be very high, and for conductor, these bands overlap each other.

The conduction band carries the electrons that conduct electricity, but the valence band has all the electrons in the ground state. Whether they go into the conduction band depends on the temperature and the energy gap between the bands. In a conductor, these bands overlap, and hence many electrons can become conducting. Thus, Band Theory explains distinction between metals and insulators, which Free Electron theory cannot do (since it assumes all valence electrons become conducting). Calculations are be performed to see which materials will have big energy gaps and which will have overlapping bands.