Free electron model in solidstate physics, the free electron model is a simple model for the behaviour of valence electrons in a. In his papers, he applied the freeelectron model almost exclusively to benzene and related aromatic systems. So, there collective behavior is not describe by classical maxwell. Freeelectron lasers which are also called ubitrons when applied to microwaves millimeter waves consist of an electron beam propagating through a periodic transverse magnetic field called a wiggler or undulator that induces motion perpendicular to the axis of symmetry. 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. 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 valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal.
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. According to the classical free electron theory the value of specific heat of metals is given by 4. 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. 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. Quantum free electron theory was proposed by arnold sommerfeld. In order to explain electrical conductivity in metals, lorentz and drude put forward a theory called free electron theory of metals. It is the product of drift velocity of the electron v d and collision time. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other.
According to this free electron in a metal valence electron move randdomly at room. Because an electron, even though smaller than the smallest known. Classical free electron theory permits all electrons to gain energy. Freeelectron theory of metals accessscience from mcgraw. A metal is imagined as the structure of 3dimensional array of ions in between. The new quantum mechanics, when applied to the problem of the structure of the atom with pointcharge electrons, does not give results in agreement with experiment.
Give the assumptions of the classical free electron theory. Assumptions or salient features in classical free electron theory the classical free electron theory is based on the following postulates. The treatment of a metal as containing a gas of electrons completely free to move within it. Energy spectrum of a nearlyfree electron model in 1d the eigenstates of free problem in 1d. The theory of electrons, and its applications to the phenomena of light and radiant heat by lorentz, hendrik antoon, 18531928. The classical free electron theory was introduced by p. Chapter 4 electronic structure the electronic properties of matter determines its macroscopic behavior. From the classical free electron theory the value of specific heat of metals is given by. The weak periodic potential causes a distortion of the fermi circle of a twodimensional electron gas as it approaches the zone boundary. Drude also assumed that the electrons would be scattered by every atom i. From atomic theory, we are used to the idea that different electronic. Drudes theory of metals used a classical free electron model.
Electron theory states all matter is comprised of molecules, which in turn are comprised of atoms, which are again comprised of protons, neutrons and electrons. 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 gaseous molecules so that these electrons are called free electron gas. It could not explain the negative temperature coefficient of resistivity for certain solids 2. This document is highly rated by civil engineering ce students and has been viewed 10656 times. Mar 18, 2018 drude theory of conduction basics of free electron theory and electrical conductivity part 1 duration. Electricity can be defined, then, as charged matter. Created by the best teachers and used by over 51,00,000 students.
Drudes theory treated the electrons as an ordinary classical gas. The free electron theory of metals using classical laws was developed by dude and lorentz in the beginning of last century. A schematic illustration of a freeelectron laser is shown in fig. The free electron model calculation of the lorenz factor is about twice the value of drudes and its closer to the experimental value. The freeelectron model cannot explain why some elements are metals and others insulators. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. Classical theory of freeelectron lasers book iopscience. Then sommerfelds elementary quantum mechanical theory of metals is discussed. Lecture notes theory of solids i physics mit opencourseware. 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. Free electron theory of metals nicholas research group.
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. What is classical free electron theory of metal answers. As per the classical free electron theory, free electrons in a metal are expected to behave just as gas molecules. The valence electrons form a very dense electron gas. Free electron theory classical free electron theory of metals this theory was developed by drude and lorentz and hence is also known as drudelorentz theory. In somerfield developed a new theory, in which he retained some of the features of classical free electron theory. 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.
Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. Mar 29, 2015 free electron theory of solids march 29, 2015 december 30, 2010 by mini physics electrons can be visualised as rattling around insde the metal, randomly changing direction when they collide with positive ions, much like a ball in a pinball machine. Magnetism of electrons in solids comments and corrections please. The subject of electron tubes has been divided into two signal subcourses. 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. Hence, classical free electron fails to explain the temperature dependence of electrical conductivity. Transition metals, such as iron, have partially filled electronic d states and are not treated by the freeelectron model. Free electron theory of solids march 29, 2015 december 30, 2010 by mini physics electrons can be visualised as rattling around insde the metal, randomly changing direction when they collide with positive ions, much like a ball in a pinball machine. The free electrons, considered identical to the outermost, or valence. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Free electron theory of conductor was proposed by p. The nearlyfree electron model university of oxford. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in selection from engineering physics book.
However, the free electron circles c 2 and c 3 intersect the zone boundaries. Classical free electron theory of metals engineering. 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. In 1998 he joined the faculty of the university of hawaii where he is currently an associate professor of physics. Besides, in the freeelectron model electrons can travel long distances. Electron theory definition of electron theory by the free. A molecule is the smallest part of matter which can exist by itself and contains one or more atoms. In classical free electron theory, we use maxwellboltzman statics which permits all free electrons to gain energy. B m s institute of technology classical free electron theory. What is the main difference between classical free. Classical free electron theory is modeled by drude lorentz to explian elctrical conductivity in metals.
Drude theory of conduction basics of free electron theory and electrical conductivity part 1 duration. According to this theory, the free electrons obey quantum laws. Apr 10, 20 the phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. His current research interests include the theory and design of novel optical resonators for highresolution free electron laser spectroscopy, xray generation and highfield physics. Electrons are treated as point like particles, charge fields, and as gas molecules in an electron gas 2. It is free to move throughout the volume of the metal.
Find materials for this course in the pages linked along the left. Because there is an energy gap between the electron states in the zone. In the lectures we have derived two simple rules, which are away from brillouinzone boundaries the electronic bands i. Pdf free electron theory 201516 vtu shashank mohan. With this heat capacity the free electron model is also able to predict the right order of magnitude and temperature dependence at low t for the seebeck coefficient of the thermoelectric effect. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the. The valence electrons of atoms are free to move about the whole volume of the metal, like the molecules of a perfect gas in a container. Wiedemannfranz law relationship between thermal conductivity k and electron conductivity s. The average distance traveled by a free electron between any two successive collisions in the presence of an applied field is known as mean free path. In solidstate physics, the free electron model is a simple model for the behaviour of. What is difference between classical theory and quantum. That time the valance electrons in metals were regarded as the noninteracting particles of an ideal gas. Classical free electron theory, physics experts mind. 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.
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. Apr 22, 2020 classical free electron theory of metals engineering physics edurev notes is made by best teachers of civil engineering ce. 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. Dec 03, 2012 for the love of physics walter lewin may 16, 2011 duration. Every investigation based on them, and only such one, is to be denoted as belonging to the framework of the theory of electrons. This is totally inexplicable within the free electron model.
Classical free electron theory could not explain many physical properties. Electron theory synonyms, electron theory pronunciation, electron theory translation, english dictionary definition of electron theory. Quantum free electron theory of metals science key. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. Some appreciation of the term of relaxation time dt. But quantum free electron theory permits only a fraction of electrons to gain energy. Electron theory definition of electron theory by the. Although this is an unsupervised subcourse, you should always feel free to seek assistance from your supervisor, peers or someone knowledgeable on the subject matter whenever you encounter difficulty. The dude model is the application of kinetic theory to electrons in a solid. 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 hence, classical free electron fails to explain the temperature dependence of electrical conductivity. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. What is the main difference between classical free electron theory and quantum free electron theory. Free electron model a free electron model is the simplest way to represent the electronic structure of metals.
The theory has been developed in three main stages. Atomic selectrons are delocalised due to overlap of outer orbits. Physics 12, classical free electron theory by patrick bruskiewich. The collection of valence electrons from all the atoms in a given piece of metal forms electron gas. According to this theory, the metals containing free electrons obey the laws of classical mechanics. This had electron speeds which were classically thermal 1 2mv 2 3 2kbt, i. 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. Several investigators have proposed a spinning ring model of the electron with varying success and limitations. Dec 09, 20 these four statements represent the general fundamental hypotheses of the theory of electrons.
Put free electrons into a very wide potential well the same size as. Freeelectron theory of metals article about freeelectron. Chapter 6 free electron fermi gas national tsing hua. This theory is called quantum free electron theory. Mar, 2017 start free trial sign in engineering physics by s. Unit iii free electron theory engineering physics dr. Treating the nearly free electron model using degenerate perturbation theory has been shown on the blackboard during lectures 3. Engineering physics ii unit 1 conducting materials notes. According to free electron model fem, the valance electrons are responsible for the conduction of electricity, and for this. Free electrons in a metal resemble molecules of a gas. The electrons follow the fundamental coulombs inverse square law.
Unit1 classical free electron theory physics youtube. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. Page 3 mobility of electrons the mobility of electrons is defined as the magnitude of drift velocity acquired by the electron in a unit field. Free electron theory of solids mini physics learn physics. Drude model conductivity frequency dependence plasma. Drude model fails to predict hall and conductivity for all metals except for alkaline metals metal li na k ag au al inr h en 0780. This is true for any k,but a periodic perturbation has nonzero matrix elements only between particular states. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals. Chapter 3 magnetism of the electron trinity college, dublin. The fundamental hypotheses of the theory of electrons. In solidstate physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of a metallic solid. So, that one can think of free electrons which are not strongly interacting free electron for free. Metals drudes classical theory theory by paul drude in 1900, only three years after the electron was discovered.
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