Electron Theory Of Metals

Free Electron Theory Introduction:-

Drudge and Lorentz developed classical free election theory to explain many special properties like conduction of electricity, thermal conductivity, magnetic properties etc of metals later Somerfield improved the version by applying quantum principles next Bloch started band theory which consider the interaction between the positive ions centres and the free electrons. The band theory could explain the behavior of solids with respect to the conduction of electricity through them.

Free electron theory is required because only electrons are responsible for conduction in metals such electrons which responsible for conduction phenomenon are called free electrons or conduction electron.

Classical free electron theory or electron gas model

Drudge and Lorentz proposed free electron theory of metals on the basis of some assumptions

1) In conductors (metals), there are large numbers of free electrons moving freely within the metal i.e. the free electrons or valence electrons are free to move in the metal like gaseous molecules, because nuclei occupy nearly 15% metal space and the remaining 85% space is available for the electrons to move.

2) Since free electrons behave like gaseous molecules, applying the laws of kinetic theory of gases. The mean K.E of a free E is equal to that of a gas molecule at same temperature.

3) In the absence of any electric field, the ES move randomly while undergoing scattering at +ve ion centers. The collisions are regarded as elastic (no loss of energy).

4) The electron speeds are distributed according to the max well- Boltzmann distribution law.

5) When an electric filed is applied, the free electrons are accelerated in a direction apposite to that of the field.

6) The free electrons are cornfield to the metal due to surface potential

7) The electrostatic force of attraction B/W the + ve ion cores and the free electrons is assumed to be negligible. The approximation is justified in the sense that the free electrons are move at a greater speed as they approach the electrons is also neglected in the concept of free electron theory.

Rms Velocity Of Free Electrons:-

i.e the relaxation time is defined as the time required for the electrons to reduce its velocity to 1/e of its initial value (directional velocity)