Sommerfield''s free electron gas model, Physics

Q. Give the basic assumptions made in free electron model of solid.


Write down basic postulates of Sommerfield's free electron gas model. Show that the number of energy states per unit energy is given by g(E) mean by Fermi energy level.

Ans. Sommerfield's Free Electron Gas Model

The theory of electrical conductivity in metals based on quantum theory of free electrons was given by sommerfield. According to this theory, the electron is treated as a wave. Therefore, the electrons are bound to obey the quantum concepts. Sommerfield kept the other concepts of the classical free electron theory, which are as follows :

(a)  Since the electron is behaving as a wave, the velocity and the energy distribution of the electron is explained by Fermi Dirac statistics.

(b)  The electrons are treated as free to move anywhere within the crystal.

(c)  There is negligible electrostatic interaction between the electrons and the lattice ions.

(d)  The free electrons are totally responsible for electrical conductive nature of the material.

(e)  Negligible interaction between the electrons.

(f)   The effect of the electric field is to change the distribution of electrons, the electrons move away from the field with a constant velocity and this velocity known as drift velocity.

(1)    Success of Free Electron Theory

1.    The quantum free electron theory is successful in explaining most of the properties of metal such as the electronic specific heat, electrical conductivity. Electronic par magnetism, Fermi energy and thermionic emission.

2.    The most important feature of this theory is that even at very low temperatures the electrons have appreciable energy because of the Pauli exclusion principle onlt those electrons which are close to the Fermi energy take part in excitations either due to thermal energy or due to extreme electric and magnetic fields.

3.    Even all success, it fails to explain the positive value of hall coefficient and some transport properties of metals.

(2)      Density of Energy States

The total number of available electron state per unit energy range is called density of available electron stat and the number of states the t are filled with electrons per unit energy I s called density of filled electron state.

In order to know the actual number of electron within a given range, we have to know the number of states in the system which has the energy consideration.

(3)      Calculation of N (E) Sphere

(4)      Fermi Energy, Fermi Level and Fermi Surface : At absolute zero temperature, all states up to a surface are filled with electrons and those above are empty from the surface is called Fermi surface. It simply means that a level which separate the filled unfilled energy levels at 0 K, above the level all the energy states are unfilled and below this all state are completely filled, this level is called Fermi level.

Posted Date: 7/11/2012 3:25:14 AM | Location : United States

Related Discussions:- Sommerfield''s free electron gas model, Assignment Help, Ask Question on Sommerfield''s free electron gas model, Get Answer, Expert's Help, Sommerfield''s free electron gas model Discussions

Write discussion on Sommerfield''s free electron gas model
Your posts are moderated
Related Questions
The weighted rod floats with 6 cm of its length under water [density 1000 kg/m3]. What length is under the surface when the rod floats in brine [density 1200 kg/m3].

Explain power of a lens. What is the principle of an optical fibre? What is a thin prism? Describe angular dispersion between two colours for a prism.

Q. Measurement of Wavelength of Monochromatic Light? Monochromatic Light is allowed to fall on plate G 1 . The M.I. is adjusted for circular fringes. For this mirror M 1 is ma

Regard as an electron and a proton at an instant in time to be at a separation of 5 cm from each other. Presume the pair to be totally isolated from its surroundings in the vacuum

Interaction of X-rays With Matter Elaborating the 3 principle modes through which X-rays interact along with matter. Photoelectric effect, Pair Production Compton Effect,. Sel

definetion and abstrec of positive clliper?

Binding energy of a system is described as the energy released when its constituents are brought from infinity to form the system. It can also be explained as the energy required s

A circuit which employs a DIRECT CURRENT source has a branch which has a capacitor.  After the circuit has reached a steady state, what is the magnitude of the current in the c

Can multiple illuminators change colors simultaneously? Yes. Usually the standard disc rotating motors are of the synchronous form, very reliable, and geared to the most suffi

Explain about the intermodal dispersion in optical fibers. Intermodal Dispersion Δτ im ) This dispersion arises even when light that is launched into the fiber is s