Classical free electron theory, Physics

  • Classical free electron theory:

The free electron theory of metals using classical laws was developed by Dude and Lorentz in the beginning of last century. That time the valance electrons in metals were regarded as the non-interacting particles of an ideal gas. The dude model is the application of Kinetic theory to electrons in a solid. It assumes that the material contains immobile positive ions and an electron gas of classical, non-interacting electrons of density n. Motion of these positive ions and electrons is damped by a fractional force due to their collisions with each other. This motion is characterized by a relaxation time 'τ'.

To obtain some useful results for conduction electrons in metals, let us start with some classical ideas.

(1)         In the absence of an applied electric field, the electrons move in random directions. They collide with random impurities and/or lattice imperfections in the crystal. These imperfections arise from thermal motion of ions about their equilibrium position.

(2)         The frequency of electron-lattice imperfections collisions can be described by a means free path λ. Mean free path (λ) can be defined as the average distance that an electron travels between collisions.

(3)         When an electric field is applied. The electron drifts in the direction opposite to that of the field. The speed with which electrons drift is called drift speed.

(4)          The drift speed is much less than the effective instantaneous speed v of the random motion. Let us now sound system with an example electric field. A given copper Rod of uniform cross-section (say 1sq-m) is subjected to a field. The possessive nature of electrons is now suppressed. The random motion is discouraged the charged electrons prefer to have a unidirectional motion. The direction of this motion is opposite to the direction of the applied electric field as sketched. Now the free electrons will bump into a caution of the lattice from time to time. Let the average time between such collisions be τ sec. immediately after a collision we suppose that the velocity of the electrons averages to zero. It means that the electron has no money of the momentum acquired from the field and that is thermal velocity averages to zero it means that its electron has no money of the momentum that its thermal velocity averages to zero. In a time τ sec the electron will at in a velocity given by:

                                                      Vd = aτ

 Where Vd is called drift velocity, and the magnitude of a=e E/m

Thus Vd= -eEτ/m

Usually the term eτ/m is replaced by μ. Μ is called the mobility of charge carriers. It can be defined as the drift velocity in unit field. Thus

                           Vd= -μE

If n is the density of electron and -e is the charge of the electron, then charge flowing through unit area in one second is given by

                                                 Jx = δq/aδt

Here δq= net quantity of charge flowing an area A in time δT and

Δq = -enAδx

Jx is also called the current density.

σ =neμ

in a metal, when temperature increases, n remains constant. But μ decreases as lattice scattering increases and therefore conductivity decreases.

Posted Date: 7/21/2012 7:32:50 AM | Location : United States







Related Discussions:- Classical free electron theory, Assignment Help, Ask Question on Classical free electron theory, Get Answer, Expert's Help, Classical free electron theory Discussions

Write discussion on Classical free electron theory
Your posts are moderated
Related Questions
did the resistance of an ohmic conductor depends on the applied voltage

A transformer takes a current of 0.8A when its primary is connected to a 240 volt, 50Hz supply, the secondary being on open circuit. If the power absorbed is 72 watts, Determi

Each particle produces a gravitational field around it which exerts the gravitational force on each of the other particles present within this region. The portion around a point ma

A constant force of 10N is applied perpendicular to rod placed on 2 parallel rails .If the rod is having a resistance 10ohm but rails have zero resistance then maximum speed of rod

Q. What are the methods of inducing emf in a circuit? The induced emf is able to be produced by changing a) The magnetic induction (B) b) Area enclosed by the coil (A) f

why at critical temperature in superconductors resistance becomes zero? Solution) For conductors as the temperature increases their rasistance increases and as temperature decreas

#how entropy tells which process is spontaneous and which is non spontaneous.i also wana know that although 2nd law of thermodynamic is for heat engine and heat pump how it is rela

describe the construction and working of michelson''s interferometer explain the formation of circular fringes how will you use these fringis in the determination of difference in