Perturbation theory and nearly free electron model pdf lecture notes. It is possible that many electron may possess same energy. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. This theory explains photo electric effect, compton effect and block body radiation. Quantum size effect and features of nanotechnology materials duration. It did not apply to metals with closed fermi surfaces, i. The model can be very predictive when applied to alkali and noble metals. This theory explains the specific heat capacity of materials. But quantum free electron theory permits only a fraction of electrons to gain energy. The electronic structure discussion group esdg is a regular informal meeting of researchers from various cambridge university departments and several commutable universities in london who are involved in research into computational electronic structure theory. Mod01 lec9 the free electron theory of metals duration. B m s institute of technology classical free electron theory. The energy values of the free electrons are discontinuous because of which the energy levels are discrete. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role.
This document is highly rated by electronics and communication engineering ece students and has been viewed 1429 times. This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. The development of the quantummechanical electron theory of. Handout 2 sommerfeld model for metals free fermion gas. They follow maxwell boltzmanns distribution to eva. Quantum free electron theory of metals pdf the turn of the twentieth century, of a free electron theory of metals and the writing by arnold sommerfeld and. 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. 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. This page contains materials for the session on the band theory of solids. But according to quantum theory, the free electrons occupy different energy levels, up to fermi level at 0 k. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i.
Some appreciation of the term of relaxation time dt. This document is highly rated by engineering mathematics students and has been viewed 800 times. Srit unit iii free electron theory engineering physics. Most books thus drop b by assuming electrons to carry spin and state that a is then broken. Electrons are treated as point like particles, charge fields, and as gas molecules in an electron gas 2. Ravindran, sommerfield model for free electron theory uio. Ravindran, phy075 condensed matter physics, spring 20 16 july. A natural step was to formulate a quantum theory of electrons in metals. Quantum free electron theory of metals science key. Effect of impurity and temperature on electrical resistivity of metals. The classical free electron theory drude and lorentz proposed this theory in 1900. His approach is based upon quantization of electrical energy levels. This theory is called quantum free electron theory.
Note that since the imaginary part gets very large for frequencies below the plasma frequency, it. A metal is imagined as the structure of 3dimensional array of ions in between. Classical derivation of ohms law and drude conductivity. 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. 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. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university does not say anything about the electron energy distribution in metalsare all electrons moving around with about the same energy. Apr 19, 2020 quantum free electron theory engineering mathematics notes edurev is made by best teachers of engineering mathematics. It features a 1hour lecture video, and also presents the prerequisites, learning objectives, reading assignment, lecture slides, homework with solutions, and resources for further study. Jun 15, 2018 neglecting the electron electron interaction and the electron ion interaction, it appears as if the electrons move in a confined box with periodic collision with ions in the lattice. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university does not say anything about the electron energy distribution in metals are all electrons moving around with about the same energy. So, that one can think of free electrons which are not strongly interacting free.
Doublewell and tightbinding models pdf lecture notes. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. Qmc in cambridge and around the world quantum monte carlo. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. Introduction to the electron theory of metals the electron theory of metals describes how electrons are responsible for the bonding of metals and subsequent physical, chemical and transport properties. Ii, iii, and iv, to the test areas of transport phenomena resulting in band theory, magnetism, and superconductivity. Kronig penny model according to quantum free electron theory of metals, a conduction electron in a metal experiences constant or zero potential and free to move inside the crystal but will not come out of the metal because an infinite potential exists at the surface. The free electrons, which constitute the electron gas can have continuous energy values. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure.
The quantum free electron theory somerfield developed this theory in 1928. The treatment of a metal as containing a gas of electrons completely free to move within it. Esdg meetings are intended to promote the exchange of ideas between. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. Text books on quantum mechanics usually claim that at least noninteger spins are only possible in quantum mechanicsthere is some controversy on this, though. The development of the quantummechanical electron theory of metals. Sommerfelds free electron theory of metals physics. Topics include heisenbergs uncertainty principle, normalization, stationary states, wave and group velocities, mean values, and variational method. Sommerfeld 1928 applied the principles of quantum mechanics to classical free electron theory. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. It could not explain the negative temperature coefficient of resistivity for certain solids 2. Quantum theory for dielectric properties of conductors a. Explain the quantum free electron model of metals in terms of paulis exclusion principle calculate the energy levels and energylevel spacing of a free electron in a metal metals, such as copper and aluminum, are held together by bonds that are very different from those of molecules. According to this theory, the metals containing free electrons obey the laws of classical mechanics.
In solidstate physics, the free electron model is a simple model for the behaviour of. Whereas electrons are quantum particles which obey electrons are known as. The main assumptions of classical free electron theory are. So it leads to much larger predicted quantities than that is actually observed. 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 development of the quantum mechanical electron theory of metals. The electrons travel with a constant potential inside the metal but confined within its boundaries. Thermal properties of the free 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 27 48. These limitations of the classical theory were overcome to a large extent by sommerfeld who argued that free electrons in a metal behave as quantum. Plot of the real and imaginary parts of the index of refraction n. Later, quantum mechanics became the basis for the theory of most of the general properties of simple metals such as sodium, with one free electron per. Behavior of free electron is different from electron in the potential field of the crystal as current is due to flow of charge, electron behavior in external electric field is important 9.
According to this theory, the metals containing the free electrons obey the laws of classical mechanics. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. Pdf free electron theory 201516 vtu shashank mohan. According to this theory, the free electrons obey quantum laws. Metal that contains free electrons wondering around positive cores.
Sommerfield model for free electron theory 9 the salient features of quantum free electron theory sommerfeld proposed this theory in 1928 retaining the concept of free electrons moving in a uniform potential within the metal. Quantum free electron theory classical free electron theory could not explain many physical properties. The following assumptions of classical free electron theory holds good in quantum free electron theory also. Although the free electron model is a great oversimplification of the reality, surprisingly in many cases it works pretty well, so that it is able to describe many important properties of metals. The electrons follow the fundamental coulombs inverse square law. According to this theory the free electrons obey quantum laws. Atomic selectrons are delocalised due to overlap of outer orbits.
Equation ii is the equation of velocity of electrons, hence c has dimension of velocity, and can only be random velocity of electron which it had at the initial stage when no field was applied. What is difference between classical theory and quantum. Hence, however, as we discussed earlier this random velocity averages out to zero, thus the average velocity. Crystal as infinite well potential electron confined in crystal of size. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal.
The book first discusses revision of quantum mechanics. Sommerfelds free electron theory of metals physics assignment. Then sommerfelds elementary quantum mechanical theory of metals is discussed. Sommerfeld free electron theory of metals is simple theory in which the electron can be treated as a quantum particle. This page contains selected lecture notes and inclass presentations lecture notes. Sommerfield model for free electron theory 9 the salient features of quantum free electron theory sommerfeld proposed this theory in 1928 retaining the concept of free electrons moving in a uniform potential within the metal as in the classical.
This theory gives the correct mathematical expression for the thermal conductivity of metals. The new quantum mechanics, when applied to the problem of the structure of the atom with pointcharge electrons, does not give results in. Freeelectron theory of metals accessscience from mcgraw. The classical theory had several conspicuous successes, notably the. The development of the quantummechanical electron theory. 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. Quantum theory macro particle classical physics based on newtons laws micro particle quantum physics. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in selection from engineering physics book. Classical free electron theory permits all electrons to gain energy. Later, quantum mechanics became the basis for the theory of most of the general properties of simple metals such as sodium, with one free electron per atom, magnesium with two, and aluminum with three. Fundamentals and applications of density functional theory duration. Pauli showed that in order to calculate the paramagnetism of free electrons in metals. Quantum magnetooscillations and integer quantum hall.
The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals. It has been organized mostly by mike towler since 2001. Nov 05, 2016 behavior of free electron is different from electron in the potential field of the crystal as current is due to flow of charge, electron behavior in external electric field is important 9. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. This is totally inexplicable within the free electron model. Give the assumptions of the classical free electron theory. Apr 01, 2018 drude theory of conduction basics of free electron theory and electrical conductivity part 1 duration. The free electrons, considered identical to the outermost, or valence. The classical free electron model is modified by taking into account quantum mechanics and the pauli exclusion principle.
The attraction between the electrons and the lattice ions and the. Quantum free electron theory was proposed by arnold sommerfeld. Jul 24, 20 mod01 lec9 the free electron theory of metals duration. Mod01 lec10 the free electron theory of metals electrical. Quantum free electron theory engineering mathematics notes. Drude theory of conduction basics of free electron theory and electrical conductivity part 1 duration. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. Drude model fails to predict hall and conductivity for all metals except for alkaline metals. Since most metals have open fermi surfaces, this theory of the linear magnetoresistance was quite satisfactory. According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. Neglecting the electronelectron interaction and the electronion interaction, it appears as if the electrons move in a confined box with periodic collision with ions in the lattice.
All due to the free electrons of the metallic bond outline classical drude theory of metals successes and limitations of the classical model sommerfeld theory of metals quantum statistics and semi. Thermal conductivity of metal and wood thermodynamics. Freeelectron theory of metals article about freeelectron. Free electron theory of metals nicholas research group. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium.
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