This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. The electrons move in a constant potential inside the. Prominent examples are the alkali metals and aluminum. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. Electron theory definition of electron theory by the free. Conductivity, hall effect and other transport phenomena will be treated separately in chapter 11. Mar, 2017 start free trial sign in engineering physics by s. Engineering physics ii unit 1 conducting materials notes. Classical free electron theory is modeled by drude lorentz to explian elctrical conductivity in metals. The main assumptions of quantum free electron theory are, the energy levels of the conduction electrons are quantised.
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. About that time, geometrical terms such as extremal sections, curvatures, diameters, limiting points began to appear in papers on the electron theory of metals. Classical free electron theory permits all electrons to gain energy. 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. Free electron theory of metals request pdf researchgate. According to this free electron in a metal valence electron move randdomly at. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. What is classical free electron theory of metal answers. 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.
Quantum free electron theory was proposed by arnold sommerfeld. Write down the drawbacks of classical free electron theory. The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals. What are the drawbacks of classical free electron theory. 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. Classical derivation of ohms law and drude conductivity. Drude theory of conduction basics of free electron theory and electrical conductivity part 1 duration. Energy of a free electron, for an electron density n specific heat. The classical theory had several conspicuous successes, notably the. This theory is called quantum free electron theory. Mod01 lec9 the free electron theory of metals duration. The classical free electron theory is based on the following postulates.
They follow maxwell boltzmanns distribution to eva. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. Classical free electron theory of metals civil engineering. Give the assumptions of the classical free electron theory. Electronic heat capacity, ce is overestimated by a factor of 100 in the classical free electron theory of metals because, all electrons in a metal is assumed to be responsible for the uptake of energy. It was developed in 1927, principally by arnold sommerfeld, who combined the classical drude model. In solidstate physics, the free electron model is a simple model for the behaviour of. The electrical conductivity of semiconductor and insulator cannot be explained by this theory. 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.
Mar 17, 2020 classical free electron theory of metals civil engineering ce video edurev is made by best teachers of civil engineering ce. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. It turns out that the nearly free electron approximation is quite reasonable for simplemetals withpredominant s. From the classical free electron theory the value of specific heat of metals is given by. Apr 10, 20 the phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. 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 theory, but treated the electrons as obeying the laws of quantum mechanics. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. 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. Srit unit iii free electron theory engineering physics.
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. Free electrons in a metal resemble molecules of a gas. Specific heat in quantum free electron theory in classical theory, specific heat of the electron gas c 32 k. Introduction to the electron theory of metals uichiro. The electrons follow the fundamental coulombs inverse square law. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. The distribution of electrons in various allowed energy levels occur as per pauli exclusion principle. Sommerfelds free electron theory of metals physics. But quantum theory states that only a few electron absorb the supplied energy. Put free electrons into a very wide potential well the. In a metal the available free electrons are fully responsible for electrical conduction. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. The free electrons, considered identical to the outermost, or valence. The model of the free electron theory is presented.
This paper continues an earlier study of the first phase of the development from 1926 to 1928 devoted to finding the general quantummechanical framework. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. The model, which is an application of kinetic theory, assumes that the microscopic behaviour of electrons in a solid may be treated classically and looks much like a pinball machine, with a sea of constantly jittering electrons bouncing. Free electron theory of metals conductivity electrical. The classical free electron theory of metals drude lorentz theory of metals postulates. The statistical distribution deals with the question as to what is the probability occupation of a particular energy level. Freeelectron theory of metals accessscience from mcgraw. As per the classical free electron theory, free electrons in a metal are expected to behave just as gas molecules. The simplest model of a metal is the free electron model. A model of a metal in which the free electrons, that is, those giving rise to the conductivity, are regarded as moving in a potential due to the metal ions in the lattice and to all the remaining free electrons which is approximated as constant everywhere inside the metal.
Assumptions postulates of quantum free electron theory 1. In order to explain electrical conductivity in metals, lorentz and drude put forward a theory called free electron theory of metals. However, the following assumptions of classical electron theory continue to be applicable in quantum free electron theory also. The main assumptions of classical free electron theory are. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role.
The valence electrons form a very dense electron gas. Engineering physics ii unit 1 conducting materials. These free electrons are, therefore, also referred to as free electron gas and the theory is accordingly named as free electron gas model. Electrons are treated as point like particles, charge fields, and as gas molecules in an electron gas 2. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. The discussions assume the readers familiarity with the material pertaining to appendixes b, c, d, and e. B m s institute of technology classical free electron theory. An important electronic property, namely the electron density at the wignerseitz atomic cell boundary, has been related to the abrasive wear resistance data in the case of pure metals. Based on the debroglie wave concept, he assumed that a moving electron. Drude model conductivity frequency dependence plasma. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals. Classical theory states that all free electrons absorb the supplied energy. 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. The book starts with the basics of one electron band theory and progresses to cover high tc superconductors and quasicrystals.
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. Effect of impurity and temperature on electrical resistivity of metals. The free electron model considers that metals are composed of a quantum electron gas where ions. This page contains materials for the session on the band theory of solids.
Some appreciation of the term of relaxation time dt. Free electron theory of metals nicholas research group. The behaviour of free electrons moving inside the metals is considered to be similar to that of atoms or molecules in perfect gas. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. Electron theory synonyms, electron theory pronunciation, electron theory translation, english dictionary definition of electron theory. Solid state, by providing a large and ready number of concrete prob. Thus, reason for failure of classical free electron theory to account for low specific heat of metals is now understood. It could not explain the negative temperature coefficient of resistivity for certain solids 2.
In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. Quantum free electron theory of metals science key. According to the classical free electron theory the value of specific heat of metals is given by 4. 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. Ravindran, phy075 condensed matter physics, spring 20 16 july.
The metals form a unique type of bonding known as metallic bonding and form the lattice structure. 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. Metals drudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. 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. But experimentally it was found that, the contribution to the specific heat of a metal by its conduction electrons was c v 104rt which is for lower. Mod01 lec10 the free electron theory of metals electrical. 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 an atom electrons revolue around the nucleus and a metal is composed of such atoms.
Engineering physics ii unit 1 conducting materials notes topic covered. 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. Put free electrons into a very wide potential well the same size as the. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. Conductors classical free electron theory of metals electrical and thermal conductivity wiedemann franz law lorentz number draw backs of classical theory quantum theory fermi distribution function effect of temperature on fermi. The authors accessible approach allows for comparisons with experimental results as much as possible. Jun 14, 2001 the electron theory of metals describes how electrons are responsible for the bonding of metals and subsequent physical, chemical and transport properties. All metals share common properties excellent electrical conductors excellent thermal conductors shiny when polished 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.
Sommerfelds free electron theory of metals physics assignment. Metals, such as copper and aluminum, are held together by bonds that are very different from those of molecules. The development of the quantummechanical electron theory of. 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. So it leads to much larger predicted quantities than that is actually observed. To assign the peak in the optical absorption spectrum of alkalis observed in figure 1. Drudes theory treated the electrons as an ordinary classical gas.
Molar specific heat hence, thermal conductivity k 12 n k. As examples of applications the fieldemission microscope and quartzhalogen lamps are discussed. 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. But quantum free electron theory permits only a fraction of electrons to gain energy. So, that one can think of free electrons which are not strongly interacting free electron for free in the. The valence electrons of metallic atoms are free to move in.
Atomic selectrons are delocalised due to overlap of outer orbits. In metals there are large number of free electrons moving freely in all possible directions. 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. What is difference between classical theory and quantum. This theory was developed by drude and lorentz during 1900 all the atoms are composed of and hence is also known as drudelorentz theory. This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. 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. Freeelectron theory of metals article about freeelectron. According to this theory, a metal consists of electrons which are free to move about in the crystal like molecules of a. Created by the best teachers and used by over 51,00,000 students. Classical free electron theory of metals engineering.
This text presents a complete account of electron theory in both periodic and nonperiodic metallic systems. This video is highly rated by civil engineering ce students and has been viewed 1140 times. Unit1 classical free electron theory physics youtube. In this chapter the free electron theory of metals as developed by sommerfeld and others will be discussed. Rather than sharing and exchanging electrons, a metal is essentially held together by a system of free electrons that wander throughout the solid. B m s institute of technology approved by aicte new. The valence electrons of atoms are free to move about the whole volume of the metal, like the molecules of.
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