FREE ELECTRON THEORY.pptx

CLASSICAL FREE ELECTRON THEORY

1. FREE ELECTRON THEORY BY BY THANUSH.S 22ECR214

2. Current Density It is the current flowing across unit area of a metal in the presence of an external electric field. It is given by j = nevd where n is the carrier concentration, e is the charge of electron and vd is the drift velocity of free electrons. Its unit of measurement is Ampere/metre2.

3. Mean Free Path & Mean Free Time

4. Postulates of Classical Free Electron Theory • Metals consist of atoms, which in turn, consist of a nucleus and electrons. • Valence electrons are free and the metal is visualized as an array of ions permeated by a gas of free electrons. • In the absence of an electrical field, electrons move in random directions colliding with ions or free electrons. • In an electrical field, free electrons are accelerated and move in the opposite direction compared to that of the electric field. • Electron velocities obey Maxwell–Boltzmann distribution function. • Free electrons move without interaction between them and they obey the laws of classical kinetic theory of gases. • Free electrons move in a uniform potential field since ions are fixed in the lattice.

5. MERITS OF CLASSICAL FREE ELECTRON THEORY

6. DRAWBACKS OF CLASSICAL FREE ELECTRON THEORY • It fails to explain the photoelectric effect, Compton effect, black body radiation, etc. • It gives a value of 4.5R for the specific heat of metals. But, the experimental value is only 3R. • It does not explain the ferromagnetism. • The long mean free paths (more than one cm) of the free electrons at low temperatures cannot be explained on the basis of the classical theory. • Experimental results shows that paramagnetism of metals is independent of temperature which deviates from classical result that paramagnetic susceptibility is inversely proportional to the temperature.

7. ELECTRICAL CONDUCTIVITY Electrical conductivity refers to the ability of the metal to conduct electrical energy.

8. QUANTUM FREE ELECTRON THEORY The important assumptions made by Sommerfeld are given below: • The free electrons move in a constant potential inside the metal and are confined within defined boundaries. • The eigen values of the conduction electron are quantized. • The electrons are considered to posses wave nature. • In the various allowed energy levels, distribution of electrons takes place according to Pauli’s exclusion principle. • Mutual attraction between electrons and lattice ions and the repulsion between individual electrons may be ignored.

9. DIFFERENCE BETWEEN CLASSICAL AND QUANTUM FREE ELECTRON THEORY

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