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
N-Type Substances: When a small quantity of Arsenic or Phosphorous (group VA elements) is added to silicon or Germanium, it becomes good conductor of negative charges, such a s

Physics of radiation therapy The probability  of  your  having cancer during your lifetime is about 1 out of 4 .Currently three major methods are used alone or in combination

For the magnetic circuit shown in Figure find the current I in the coil needed to produce a flux of 0.45mWb in the air gap. The silicon iron magnetic circuit has a uniform cros

one of scrooges relatives visited him in the counting house. who was it and what did he want ........................... i couldnt found a subject with reading

Q. Illustrate what are the three particles that make up an atom? Answer:- Atoms are conjured of neutrons, protons, and electrons. The protons as well as neutrons are found

Gravitational field can also be shown by lines of force. This is same in several ways as that of electric lines of forces. With one dissimilarity, electric charges are negative and

kindly send me a detailed explanation of string constraint relation on pulley based problems....2 solve it do v take a reference point from wich v take d velocities and den v go wi

Figure shows the magnetic circuit of a relay. When each of the air gaps are 1.5mm wide find the mmf required to produce a flux density of 0.75 T in the air gaps. Use the B-H cu

determine the magnitude of Poynting vector end the energy per unit time delivered to a wire of length land cross section A when electric current I flow in it