His approach is based upon quantization of electrical. As examples of applications the fieldemission microscope and quartzhalogen lamps are discussed. Classical free electron theory permits all electrons to gain energy. The classical free electron theory of metals drude lorentz theory of metals postulates. 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. 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. They follow maxwell boltzmanns distribution to eva. Free electron model a free electron model is the simplest way to represent the electronic structure 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 material. But quantum theory states that only a few electron absorb the supplied energy. So, there collective behavior is not describe by classical maxwell. According to this theory, the metals containing free electrons obey the.
In solidstate physics, the free electron model is a simple model for the behaviour of. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in selection from engineering physics book. Classical theory states that all free electrons absorb the supplied energy. Free electron theory of metals request pdf researchgate. Unit1 classical free electron theory physics youtube. The electrons follow the fundamental coulombs inverse square law. B m s institute of technology classical free electron theory. The electrical conductivity of semiconductor and insulator cannot be explained by this theory. The electrons move in a constant potential inside the. Electrons are treated as point like particles, charge fields, and as gas molecules in an electron gas 2.
Rather than sharing and exchanging electrons, a metal is essentially held together by a system of free electrons that wander throughout the solid. A valence electron in a metal finds itself in the field of all ions and that of the other electrons. Especially classical free electron theory and quantum free electron theory of metals. The simplest model of a metal is the free electron model. Classical free electron theory of metals engineering physics. As per the classical free electron theory, free electrons in a metal are expected to behave just as gas molecules.
Effect of impurity and temperature on electrical resistivity of metals. 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. According to this theory, a metal consists of electrons which are free to move about in the crystal like molecules of a. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. Apr 11, 2020 classical free electron theory of metals engineering physics edurev notes is made by best teachers of civil engineering ce. Give the assumptions of the classical free electron theory. This result was very important in the development of the theory of metals since it gave strong support to the idea of an electron gas permeating the lattice of metal ions. Atomic selectrons are delocalised due to overlap of outer orbits. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium.
Quantum free electron theory was proposed by arnold sommerfeld. 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. You can download free classical free electron theory of metals engineering physics edurev notes pdf from edurev by using search above. This document is highly rated by civil engineering ce students and has been viewed 106 times. 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. Write down the drawbacks of classical free electron theory. 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. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. Assumptions postulates of quantum free electron theory 1. The development of the quantummechanical electron theory. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems.
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 model of the free electron theory is presented. In the classical free electron model the electron loses energy on the average in. 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. Engineering physics ii unit 1 conducting materials.
The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. Free electrons are valence electrons of the atoms just like in the classical theory. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. Metals, such as copper and aluminum, are held together by bonds that are very different from those of molecules. The free electrons, considered identical to the outermost, or valence. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. From the classical free electron theory the value of specific heat of metals is given by.
Sommerfelds free electron theory of metals physics. 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. Based on the debroglie wave concept, he assumed that a moving electron. 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.
Srit unit iii free electron theory engineering physics. 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. Classical free electron theory is modeled by drude lorentz to explian elctrical conductivity in metals. Assumptions or salient features in classical free electron theory the classical free electron theory is based on the following postulates. What are the drawbacks of classical free electron theory. The development of the quantummechanical electron theory of metals. The main assumptions of classical free electron theory are. B m s institute of technology approved by aicte new. Classical free electron theory could not explain many physical properties. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Put free electrons into a very wide potential well the. Free electron theory thermal motion, drift motion, drift. This theory was developed by drude and lorentz during 1900 all the atoms are composed of and hence is also known as drudelorentz theory. So, that one can think of free electrons which are not strongly interacting free electron for free.
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. Pdf free electron theory 201516 vtu shashank mohan. 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. What is difference between classical theory and quantum. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. The treatment of a metal as containing a gas of electrons completely free to move within it. This theory is called quantum free electron theory.
The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. According to this free electron in a metal valence electron move randdomly at. Hence, classical free electron fails to explain the temperature dependence of electrical conductivity. It could not explain the negative temperature coefficient of resistivity for certain solids 2. Classical free electron theory of metals engineering. Drude theory of conduction basics of free electron theory.
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. Free electron theory of metals nicholas research group. Then sommerfelds elementary quantum mechanical theory of metals is discussed. The metals form a unique type of bonding known as metallic bonding and form the lattice structure. Quantum free electron theory of metal since classical free electron theory failed to account for the number of experimentally observed facts, sommerfeld put forward a new theory, called quantum free electron theory. According to this theory, the metals containing the free electrons obey the laws of classical mechanics.
97 836 209 537 1604 1439 464 544 1041 1544 694 1065 779 1549 1532 112 1469 721 1211 141 460 1469 1441 1042 1143 100 1072 373 592 1042 498 916 152 1249 2