Whereas electrons are quantum particles which obey electrons are known as. Plot of the real and imaginary parts of the index of refraction n. Some appreciation of the term of relaxation time dt. Jul 24, 20 mod01 lec9 the free electron theory of metals duration. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i.
The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. The classical theory had several conspicuous successes, notably the. 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 development of the quantummechanical electron theory. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. 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. This page contains materials for the session on the band theory of solids. 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. This page contains selected lecture notes and inclass presentations lecture notes. The classical free electron theory drude and lorentz proposed this theory in 1900. Mod01 lec9 the free electron theory of metals duration. Text books on quantum mechanics usually claim that at least noninteger spins are only possible in quantum mechanicsthere is some controversy on this, though.
Topics include heisenbergs uncertainty principle, normalization, stationary states, wave and group velocities, mean values, and variational method. 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. This theory explains photo electric effect, compton effect and block body radiation. 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. The electrons follow the fundamental coulombs inverse square law. 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. 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. It has been organized mostly by mike towler since 2001. So, that one can think of free electrons which are not strongly interacting free. Drude model fails to predict hall and conductivity for all metals except for alkaline metals. Metal that contains free electrons wondering around positive cores. Quantum free electron theory was proposed by arnold sommerfeld. The model can be very predictive when applied to alkali and noble metals. The attraction between the electrons and the lattice ions and the.
The treatment of a metal as containing a gas of electrons completely free to move within it. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. Note that since the imaginary part gets very large for frequencies below the plasma frequency, it. Thermal conductivity of metal and wood thermodynamics. Quantum magnetooscillations and integer quantum hall. Quantum free electron theory of metals science key. 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. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in selection from engineering physics book.
The electrons travel with a constant potential inside the metal but confined within its boundaries. A natural step was to formulate a quantum theory of electrons in metals. Give the assumptions of the classical free electron theory. This is totally inexplicable within the free electron model. 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. But quantum free electron theory permits only a fraction of electrons to gain energy.
Since most metals have open fermi surfaces, this theory of the linear magnetoresistance was quite satisfactory. This document is highly rated by engineering mathematics students and has been viewed 800 times. Most books thus drop b by assuming electrons to carry spin and state that a is then broken. The model considers that metals are composed of a quantum electron gas where ions play almost no role. According to this theory, the metals containing free electrons obey the laws of classical mechanics. It did not apply to metals with closed fermi surfaces, i. Sommerfeld 1928 applied the principles of quantum mechanics to classical free electron theory. Esdg meetings are intended to promote the exchange of ideas between.
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. A metal is imagined as the structure of 3dimensional array of ions in between. 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. Quantum free electron theory engineering mathematics notes. According to classical theory, the free electrons in a metal have random motions with equal probability in all directions.
Atomic selectrons are delocalised due to overlap of outer orbits. This theory gives the correct mathematical expression for the thermal conductivity of metals. Doublewell and tightbinding models pdf lecture notes. Freeelectron theory of metals article about freeelectron. Freeelectron theory of metals accessscience from mcgraw. Classical free electron theory permits all electrons to gain energy.
Free electron model a free electron model is the simplest way to represent the electronic structure of metals. Apr 19, 2020 quantum free electron theory engineering mathematics notes edurev is made by best teachers of engineering mathematics. The quantum free electron theory somerfield developed this theory in 1928. It could not explain the negative temperature coefficient of resistivity for certain solids 2. 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.
The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals. 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 book first discusses revision of quantum mechanics. Fundamentals and applications of density functional theory duration. 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. Ravindran, sommerfield model for free electron theory uio. Ii, iii, and iv, to the test areas of transport phenomena resulting in band theory, magnetism, and superconductivity. Free electron theory of metals nicholas research group. Free electron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. 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. Electrons are treated as point like particles, charge fields, and as gas molecules in an electron gas 2. The free electrons, considered identical to the outermost, or valence. Drude theory of conduction basics of free electron theory and electrical conductivity part 1 duration.
The free electrons, which constitute the electron gas can have continuous energy values. Sommerfeld free electron theory of metals is simple theory in which the electron can be treated as a quantum particle. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. 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. 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. The new quantum mechanics, when applied to the problem of the structure of the atom with pointcharge electrons, does not give results in. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Hence, however, as we discussed earlier this random velocity averages out to zero, thus the average velocity. They follow maxwell boltzmanns distribution to eva. Pdf free electron theory 201516 vtu shashank mohan.
The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. Ravindran, phy075 condensed matter physics, spring 20 16 july. In solidstate physics, the free electron model is a simple model for the behaviour of. 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. Quantum size effect and features of nanotechnology materials duration. The development of the quantummechanical electron theory of metals.
Sommerfelds free electron theory of metals physics. This theory explains the specific heat capacity of materials. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. B m s institute of technology classical free electron theory. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. The classical free electron model is modified by taking into account quantum mechanics and the pauli exclusion principle. According to this theory the free electrons obey quantum laws. Sommerfelds free electron theory of metals physics assignment. Then sommerfelds elementary quantum mechanical theory of metals is discussed. The following assumptions of classical free electron theory holds good in quantum free electron theory also.
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. It is possible that many electron may possess same energy. So it leads to much larger predicted quantities than that is actually observed. His approach is based upon quantization of electrical energy levels. Apr 01, 2018 drude theory of conduction basics of free electron theory and electrical conductivity part 1 duration. The development of the quantum mechanical electron theory of metals. This document is highly rated by electronics and communication engineering ece students and has been viewed 1429 times. The energy values of the free electrons are discontinuous because of which the energy levels are discrete.
In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. Crystal as infinite well potential electron confined in crystal of size. According to this theory, the free electrons obey quantum laws. Quantum theory for dielectric properties of conductors a. The main assumptions of classical free electron theory are. Perturbation theory and nearly free electron model pdf lecture notes. Handout 2 sommerfeld model for metals free fermion gas. Srit unit iii free electron theory engineering physics. 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. Qmc in cambridge and around the world quantum monte carlo. This theory is called quantum free electron theory. Quantum theory macro particle classical physics based on newtons laws micro particle quantum physics. But according to quantum theory, the free electrons occupy different energy levels, up to fermi level at 0 k.
This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. 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. 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. Pauli showed that in order to calculate the paramagnetism of free electrons in metals. Classical derivation of ohms law and drude conductivity. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. 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. What is difference between classical theory and quantum. 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. 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. Mod01 lec10 the free electron theory of metals electrical. The development of the quantummechanical electron theory of. 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 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.
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