What is Sommerfeld theory of free electrons?

The Sommerfeld free electron model treats electrons as free particles with energy dispersion ε = ℏ 2 k 2 2 m . The density of states follows from the dispersion relation by using a general procedure that is analogous to that for phonons.

What is Sommerfeld theory of metals?

Sommerfeld theory is a modified Drude model; the only significant difference being that the velocity of electrons is found from quantum statistical mechanics. First, let us quickly derive the Fermi-Dirac distribution from statistical me- chanics (canonical ensemble picture) and the Pauli exclusion principle.

What is Drude model of gas of free electrons?

The Drude model considers the metal to be formed of a collection of positively charged ions from which a number of “free electrons” were detached. These may be thought to be the valence electrons of the atoms that have become delocalized due to the electric field of the other atoms.

What are the assumptions in Drude free electron theory?

Drude model assumes that the mean electronic velocity at a point vanishes – this cannot be rigorously justified. Electrons coming from the higher temperature side will have higher energy and hence a higher speed – net motion of electrons from higher temperature side to lower temperature side.

How the quantum free-electron Sommerfeld theory is different than the classical free electron theory?

According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. But according to quantum theory, the free electrons occupy different energy levels, up to Fermi level at 0 K. So, they possess different energies and hence they possess different velocities.

What is Sommerfeld coefficient?

with Boltzmann constant , the electron density and the Fermi energy (the highest single particle energy of occupied electronic states). The proportionality constant. is called the Sommerfeld coefficient.

What are the Limitaions of electron theory given by Sommerfield?

(ii) It could not explain the distribution and arrangement of electrons in atoms. (iii) Sommerfeld’s model was unable to explain the spectra of alkali metals such as sodium, potassium etc. (iv) It could not explain Zeeman and Stark effect.

What is the significance of free electron theory?

The free electron model solved many of the inconsistencies related to the Drude model and gave insight into several other properties of metals. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role.

How is Sommerfeld coefficient calculated?

2(a). Using the experimental Sommerfeld coefficient γ N the band structure Density of states at Fermi level N(E F) can be deduced from the formula: N ( E F ) = 3 γ N π 2 k B 2 N A . where μ* is repulsive Coulomb parameter, which is typically given in the range 0.1–0.15.

What is the contribution of Sommerfeld for atomic model?

As professor of theoretical physics at Munich (1906–31), he did his most important work. His investigations of atomic spectra led him to suggest that, in the Bohr model of the atom, the electrons move in elliptical orbits as well as circular ones. From this idea he postulated the azimuthal quantum number.

What is Sommerfeld modification?

German physicist Arnold Sommerfeld modified Bohr’s theory by quantizing the shapes and orientations of orbits to introduce additional energy levels corresponding to the fine spectral lines.

How the quantum free electron Sommerfeld theory is different than the classical free electron theory?

Why does the Drude model work?

The Drude model simplifies things considerably by using classical mechanics and treats the solid as a fixed array of nuclei in a ‘sea’ of unbound electrons. Additionally, the electrons move in straight lines, do not interact with each other, and are scattered randomly by nuclei.

What are the limitations of Drude model?

Shortcomings of the Drude Model The Drude model does not take into account collisions between electrons themselves. It also does not consider electrostatic interactions between the electrons and the lattice ions. The de Broglie wavelengths of electrons with some thermal energy are on the nanometer scale.

What are the postulates of free electron theory?

Postulates of Classical free electron theory 1. In metals there are large number of free electrons moving freely in all possible directions 2. free electrons in the metals are assumed to behave like gas molecules obeying the kinetic theory of gases 3.

Who discovered free electron theory?

The free-electron model was first proposed by the Dutch physicist Hendrik A. Lorentz shortly after 1900 and was refined in 1928 by Arnold Sommerfeld of Germany. Sommerfeld introduced quantum-mechanical concepts, most notably the Pauli exclusion principle.

What is Sommerfeld’s model of the atom?

He Sommerfeld’s atomic model is an improved version of the Bohr model, in which the behavior of electrons is explained by the existence of different energy levels within the atom. Arnold Sommerfeld published his proposal in 1916 explaining the limitations of this model by applying Einstein’s theory of relativity.

What is the Bohr-Sommerfeld atomic model?

The Bohr-Sommerfeld atomic model from 1916 builds on the Bohr model from 1913 and is thus one of the older quantum theories before the development of quantum mechanics .

What is the Fermi energy of the Sommerfeld model?

The Sommerfeld model provides a good description of free electrons in alkali metals such as potassium (element K), which has a Fermi energy of ε F = 2.12 eV (data from Ashcroft, N. W. and Mermin, N. D., Solid State Physics, Saunders, 1976.). Check the Fermi surface database.

What did Arnold Sommerfeld conclude about the electron configuration?

Arnold Sommerfeld concluded that the difference in energy between the electrons – even though they were at the same energy level – was due to the existence of energetic sublevels within each level.