Classical Free Electron Theory (DRUDE – LORENTZ THEORY)

• It is a Macroscopic theory developed by Drude and Lorentz in 1900.
• A metal has nucleus with revolving electrons and the electrons move freely like molecules in a gas.
• The free electrons in a metal are moving in a uniform potential field produced by the ions.
• In the absence of electric field (E = 0), the electrons have random collisions called elastic collisions (ie., no loss of energy). In the presence of electric field (E ≠0) , the free electrons are accelerated opposite to the applied electric field.
• The electron obeys Maxwell-Boltzmann distribution of velocities and the laws of kinetic theory of gases.
• Mean collision time (τ_c ) is the time taken by the electron between two successive collisions.
• Relaxation time (τ) is the time taken by the electron to reach equilibrium position from its disturbed position in the presence of electric field. It is approximately is equal to 10^-14 sec.
• Drift velocity (V_d) is the velocity obtained by an electron in a perpendicular direction by the application of electric field.

Uses of Classical free electron theory

Classical free electron theory is used for

• Ohm’s law’s verification
• Explaining the electrical conductivity (σ) and thermal conductivity (K) of metals
• Widemann-Franz law derivation
• Explaining the optical properties of metal.

Drawbacks of Classical free electron theory

1. Classical free electron theory states that all free electrons will absorb energy, but quantum free electron theory states that only a few electrons will absorb energy.
2. This theory cannot explain the Compton effect, photo-electric effect, para-magnetism and ferromagnetism, etc.,
3. The theoretical and experimental values of specific heat and electronic specific heat are not matched in this theory.
4. By classical theory K/σT is constant for all temperatures, but by quantum theory K/ σT  is not a constant for all temperatures.
5. The Lorentz number obtained by classical theory does not have good agreement with experimental value and it is rectified by quantum theory.