The drude theory of metals the model free electron densities densityof the electron gas. Mod01 lec9 the free electron theory of metals youtube. L and a are, respectively the length and crosssectional area of the metal. Electron theory synonyms, electron theory pronunciation, electron theory translation, english dictionary definition of electron theory. Sommerfelds free electron theory of metals physics. The valence electrons of atoms are free to move about the whole volume of the. Free electron theory of metals request pdf researchgate. He derives the valence and conduction band structures for electrons in metals e.
Electrical properties of materials electronic conduction in solids. The threedimensional thermal conduction in metals j q is the thermal current density, k is the thermal. 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 mechanical. The free electrons, considered identical to the outermost, or valence. The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals. Free electron theory of metals rajendra adhikari december 9, 2015 1 drudes theory of metals in this model electrons are considered as solid spheres as gas. Nov 21, 2016 a simple model for the behaviour of charge carriers in a metallic solid. Drudes theory treated the electrons as an ordinary classical gas. Quantum free electron theory the free electrons, which constitute the electron gas can have continuous energy values. The free electron gas, however, differs from an ordinary gas in some respects. Goswamy associate professor in physics uiet, panjab university, chandigarh. The main assumptions of classical free electron theory are. Ravindran, phy075 condensed matter physics, spring 20 16 july. The amount of electrostatic potential between two points in space.
The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. Classical derivation of ohms law and drude conductivity. In this chapter the free electron theory of metals as developed by sommerfeld and others will be discussed. Drude theory of conduction basics of free electron theory. The energy values of the free electrons are discontinuous because of which the energy levels are discrete. The discussions assume the readers familiarity with the material pertaining to appendixes b, c, d, and e. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. Free electron theory of metals metals are good conductors both electrical and thermal electronic heat capacity has an additional temperature dependent contribution from the electrons. Pdf free electron theory of metals aryan gurung academia. The model can be very predictive when applied to alkali and noble metals. 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. The classical free electron theory of metals drude lorentz theory of metals postulates. The most important characteristic of a metal is its high electrical conductivity. Theory of free electrons in metals university of ioannina.
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. As examples of applications the fieldemission microscope and quartzhalogen lamps are discussed. Freeelectron theory of metals article about freeelectron. Classical drude theory of metals successes and limitations of the classical model. 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. Jun 15, 2018 free electron theory of metals june 15, 2018 february 24, 2012 by electrical4u the metals form a unique type of bonding known as metallic bonding and form the lattice structure.
If you are asking, why does the metallic bond arise, in which the electrons seem to be delocalised over the entire structure, and able to be shunted with a relatively trivial electric field difference, instead of formin. Classical free electron theory of metals engineering. Classical free electron theory of metals in order to explain electrical conductivity in metals, lorentz and drude put forward a theory called free electron theory 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 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 electrons from each atom is shared by the whole lattice. B m s institute of technology classical free electron theory. Find powerpoint presentations and slides using the power of, find free presentations research about free electron model of metals ppt. Jul 31, 2015 free electron model page 4 theory of metals free electron theory of metals band theory of solids dr. Treating the nearly free electron model using degenerate perturbation theory has been shown on the blackboard during lectures 3. In solidstate physics, the nearly free electron model or nfe model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The treatment of a metal as containing a gas of electrons completely free to move within it. The free electrons, which constitute the electron gas can have continuous energy values. Classical free electron theory of metals this theory was developed by drude and lorentz and hence is also known as drudelorentz theory. These free electrons are, therefore, also referred to as free electron gas and the theory is accordingly named as free electron gas model.
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. Mar 29, 2018 10 videos play all free electron theory universal education point basics of statistics or elementary idea of quantum statistics duration. The metals form a unique type of bonding known as metallic bonding and form the lattice structure. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium.
Freeelectron theory of metals the treatment of a metal as containing a gas of electrons completely free to move within it. May 10, 2020 explain the quantum freeelectron 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. Give the assumptions of the classical free electron theory. This document is typeset in free software latex2e distributed. Handout 2 sommerfeld model for metals free fermion gas.
Electron theory definition of electron theory by the. 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. Freeelectron theory of metals accessscience from mcgraw. Quantum free electron theory of metals science key. The classical theory had several conspicuous successes, notably the. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. The model is closely related to the more conceptual empty lattice approximation. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. Classical free electron gas classical free electron gas ohmic law vvoltage, icurrent, rresistance, rresistivity, sconductivity, and eelectric field.
The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. This document is typeset in free software latex2e distributed under the terms of the gnu general public license. Sommerfeld 1928 applied the principles of quantum mechanics to classical free electron theory. Theory of free electrons in metals elefterios lidorikis room. A metal is imagined as the structure of 3dimensional array of ions in between which, there are free moving valence electrons confined to the body of the material.
So it leads to much larger predicted quantities than that is actually observed. Cu, be using lcaomo, and then extends this approach. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. 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. It is possible that many electron may possess same energy. In the lectures we have derived two simple rules, which are away from brillouinzone boundaries the electronic bands i. 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 free electron theory was proposed by arnold sommerfeld. Band theory of electrical conductivity boundless chemistry. Free electron theory of metals nicholas research group. Band theory, where the molecular orbitals of a solid become a series of continuous energy levels, can be used to explain the behavior of conductors, semiconductors and insulators. Srit unit iii free electron theory applied physics. Especially classical free electron theory and quantum free electron theory of metals. A metal is imagined as the structure of 3dimensional array of ions in between which, there are free moving valence electrons confined to the body of the.
The classical free electron theory was introduced by p. Well examine the assumption of a constant potential. Metals drudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. Some appreciation of the term of relaxation time dt. A metal is imagined as the structure of 3dimensional array of ions in between which, there are free moving valence electrons confined to the body of.
According to this theory, a metal consists of electrons which are free to move about in the crystal like molecules of a gas in a container. The model enables understanding and calculating the electronic band structure of especially metals. When electricity flows, the electrons are considered free only because there are more electrons than there should be, and because the transition metals, such as iron, copper, lead, zinc, aluminum, gold etc. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. 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. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals. Sommerfelds free electron theory of metals physics assignment. Free electron theory of metals conductivity electrical. Mutual repulsion between electrons is ignored and hence potential energy is taken as zero. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. Assumptions or salient features in classical free electron theory the classical free electron theory is based on the following postulates. 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. Then sommerfelds elementary quantum mechanical theory of metals is discussed.
These free electrons move freely throughout the lattice and hence are termed as electron gas. The behaviour of free electrons moving inside the metals is considered to be similar to that of atoms or molecules in perfect gas. 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. According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. The model of the free electron theory is presented. Subscribe to our youtube channel to watch more lectures. 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. The density of states and the fermidirac distribution function are discussed, leading to the specific heat of the electrons, the work function, thermionic emission, and the schottky effects. Conductivity, hall effect and other transport phenomena will be treated separately in chapter 11. Quinn and others published free electron theory of metals find, read and cite all the research you need on.
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