Success of Classical Free Electron Theory

The classical free electron theory has been successfully applied to explain the various properties of metal.

1. It is used to verify Ohm’s law
2. It is used to derive Wiedemann-Franz law.
3. It explains the electrical and thermal conductivities of metals.
4. It explains optical properties of metals.
5. It correctly predicts different resistivities of various metals.

Limitations of Classical free electron theory

1. It is a macroscopic theory.
2. This theory cannot explain the electrical conductivity of semiconductors and insulators.
3. Ferromagnetism cannot be explained by this theory.
4. This theory cannot explain the Photo-electric effect, Compton effect and the black body radiation.
5. This theory cannot explain why certain solid have larger number of free electrons and thus behave as good conductor.
6. At low temperature, Lorentz number \left(\mathrm{L}=\frac{\mathrm{K}}{\sigma \mathrm{T}}\right)  is not a constant. But by classical theory it is a constant.
7. Dual nature cannot be explained.
8. Atomic fine spectra cannot be explained.
9. Classical theory states that all the free electrons will absorb energy, but quantum theory states that only few electrons will absorb energy.