Sommerfield model for free electron theory 11 success of quantum free electron theory according to classical theory, which follows maxwellboltzmann statistics, all the free electrons gain energy. The classical electron radius is a combination of fundamental physical quantities that define a length scale for problems involving an electron interacting with electromagnetic radiation. He realised the role played by pauli exclusion principle in restricting the energy values of. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. According to this theory, a metal consists of electrons which are free to move about in the crystal like molecules of a. Given its simplicity, it is surprisingly successful in.
Page 4 v d while the free electrons move towards the positive terminal in the presence of the. Quantum free electron theory of metals science key. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. The valence electrons of atoms are free to move about the whole volume of the metals like the molecules of a perfect gas in a container. So it leads to much larger predicted quantities than that is actually observed. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals.
Quantum free electron theory could successfully explain the electronic sp. Engineering physics ii unit 1 conducting materials. This simple model uses classical mechanical theory of free electron. Similarly, the heat conductivity at high temperatures was computed to be propor tional to t, but observed to go in direct proportion to t. Hence, classical free electron fails to explain the temperature dependence of electrical conductivity. It was constructed in order to explain the transport properties of conduction electrons in metals. Ine here, saw the realization that the new quantum theory could explain, at. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. Quantum theory of metals room temperature than the interatomic distance and even longer at low temperatures.
Quantum size oscillations and size effects microform. Srit unit iii free electron theory applied physics. The valence electrons of atoms are free to move about the whole volume of the. Assumptions or salient features in classical free electron theory the classical free electron theory is based on the following postulates. This theory was developed by drude and lorentz during 1900 all the atoms are composed of and hence is also known as drudelorentz theory.
Cu, be using lcaomo, and then extends this approach. Mention the drawbacks of classical free electron theory of metals. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. In 1928, by applying quantum mechanical principles, arnold sommerfeld succeeded in overcoming many of drawbacks of the classical free electron theory, while retaining all the essential features of the classical free electron theory. The uniqueness in such a type of bonding fashion lies in the fact that unlike ionic bonding and covalent bonding where the sharing of electrons is between two atoms and the electrons remain localized, in metallic bonding the bond is formed among all the atoms in the lattice and the free. In solidstate physics, the free electron model is a simple model for the behaviour of. It is free to move throughout the volume of the metal. B m s institute of technology classical free electron theory. His approach is based upon quantization of electrical energy levels. What are the merits of classical free electron theory. Ravindran, phy075 condensed matter physics, spring 20 16 july. Review of classical free electron theory, quantum free electron theory. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal.
The classical free electron theory of metals drude lorentz theory of metals postulates. Describe the classical free electron model of metals in terms of the concept electron number density. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. Department of physics question bank engineering physics ii. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other.
Mod01 lec10 the free electron theory of metals electrical conductivity duration. Ron ballinger gives todays lecture, explaining how the behavior of electrons in aggregate solids determines their electrical and thermal conductivities, optical absorption, and other physical properties. As per his investigation, the behavior of free electron in different possible energy states is explained, how the large number of electrons are disturbed in the energy states. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. Quantum free electron theory of metals pdf the turn of the twentieth century, of a freeelectron theory of metals and the writing by arnold sommerfeld and. The dude model is the application of kinetic theory to electrons in a solid. Metals drudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. The free electrons, considered identical to the outermost, or valence, electrons of free metal atoms, are presumed to be moving independently of one another throughout the. The development of the quantummechanical electron theory. Conductivity, hall effect and other transport phenomena will be treated separately in chapter 11. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. A statistical equation for describing the mean drift velocity in the direction of the field may be written. Hall effectdetermination of number and sign of charge. Drudes model 1900 is based on the kinetic theory of electrons in a metal which assumes that the material has motionless positive ions and a noninteracting electron gas.
The valence electrons of metallic atoms are free to move about the whole volume of the metals like the molecules of a gas in a container. This is one of the central results of the classical free electron theory of metals. Give the assumptions of the classical free electron theory. All due to the free electrons of the metallic bond. Theory of free electrons in metals university of ioannina. This formula is not useful for calculating the conductivity of a given metal, since it contains an unknown term called relaxation time. In an atom electrons revolue around the nucleus and a metal is composed of such atoms.
The discussions assume the readers familiarity with the material pertaining to. Free electron theory of metals request pdf researchgate. Groundstate properties of the electron gas 1 groundstate properties of the electron gas 2 the fermidirac distribution 3 thermal properties of the free electron gas 4 the sommerfeld theory of conduction in metals daniele to oli january 11, 2017 3 48. The classical free electron theory was introduced by p. Classical derivation of ohms law and drude conductivity. The properties of metals such as electrical conduction, thermal conduction, specific heat etc.
The treatment of a metal as containing a gas of electrons completely free to move within it. From the instant of sudden disappearance of an electric field across a metal, the average velocity of the conduction electrons decays. Then sommerfelds elementary quantum mechanical theory of metals is discussed. The first theory to explain the electrical conductivity of metals is classical free electron theory and it was proposed by. The metals form a unique type of bonding known as metallic bonding and form the lattice structure.
We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services. Schematic of the electronic potential assumed in the drude and sommerfeld models of metals a. Chapter 6 free electron fermi gas national tsing hua. Fermi energy and fermi factor in metals, variation of fermi factor with temperature. In this chapter the free electron theory of metals as developed by sommerfeld and others will be discussed. The collection of valence electrons from all the atoms in a given piece of metal forms electron gas. This textbook focuses on the fully classical theory of fels with application to fel oscillators and develops the fundamentals of fel theory in sufficient depth to provide both a solid understanding of fel physics and a solid background for research in the field. The smallscale details of the potential due to the ionic cores shown schematically in b are replaced by an average potential v 0. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals. Classical theory of freeelectron lasers book iopscience. Free electron theory of metals nicholas research group. Atomic selectrons are delocalised due to overlap of outer orbits. In such a picture, the ionic cores merely maintain charge. Sommerfelds free electron theory of metals physics.
The valence electrons of metallic atoms are free to move in the spaces between ions from one place to another place within the metallic specimen similar to. Chapter 5 the drude theory of metals delaware physics. Quantum free electron theory was proposed by arnold sommerfeld. Describe the classical free electron model of metals in terms of the concept electron number. Created by the best teachers and used by over 51,00,000 students. It was developed in 1927, principally by arnold sommerfeld, who combined the classical drude model with quantum mechanical fermidirac statistics and hence it is also known as the drudesommerfeld model. He derives the valence and conduction band structures for electrons in metals e. According to classical free electron theory of metals electrical conductivity is given by, from the above equation, relation between temperature and electrical conductivity is given by. It links the classical electrostatic selfinteraction energy of a homogeneous charge distribution to. This in turn will affect the way the electron gas can absorb energy from an external source. Baffling as well was the curious phenomenon of super conductivity, first observed in 1911by gilles hoist, work. The main assumptions of classical free electron theory are. Engineering physicsii classical free electron theory of. Drudes theory treated the electrons as an ordinary classical gas.