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. Energy of a free electron, for an electron density n specific heat. All due to the free electrons of the metallic bond. The collection of valence electrons from all the atoms in a given piece of metal forms electron gas. 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. Comparison classical free electron theory and quantum 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. 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. This in turn will affect the way the electron gas can absorb energy from an external source. This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. Landaus model is now known as the fermi liquid theory.
Drudes theory treated the electrons as an ordinary classical gas. Quantum free electron theory of metals science key. These free electrons move freely throughout the lattice and hence are termed as electron gas. The valence electrons of atoms are free to move about the whole volume of the metals like the. The classical free electron theory is based on the following postulates. Classical theory of freeelectron lasers book iopscience. The electron has a mass that is approximately 11836 that of the proton. The classical free electron theory was introduced by p. 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. Atomic selectrons are delocalised due to overlap of outer orbits. Apr 10, 20 the classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. This theory cannot explain the compton, photoelectric effect, paramagnetism, ferromagnetism, etc.
In an atom electrons revolue around the nucleus and a metal is composed of such atoms. Heat capacity of the electron gas classical statistical mechanics a free particle should have 3kb2. Sommerfelds free electron theory of metals physics assignment. 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. Free electron theory of metals nicholas research group. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. These electrons behaves like classical particles generally we call it electron gas.
Classical free electron theory permits all electrons to gain energy. The following assumptions apply to both the theories. Some appreciation of the term of relaxation time dt. The free electron model considers that metals are composed of a quantum electron gas. Energy of the electron is determined by the temperature of metal.
The electrons dont interact with each other rather with the much larger atomic cores. In metals there are large number of free electrons moving freely in all possible directions. Before studying the statistical formulation, we will discuss electron dynamics in a perfect crystal. 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. 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. 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. In solidstate physics, the free electron model is a simple model for the behaviour of. Molar specific heat hence, thermal conductivity k c v th. According to this theory, the metals containing free electrons obey the laws of classical mechanics. Put free electrons into a very wide potential well the same size as.
But quantum free electron theory permits only a fraction of electrons to gain energy. We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. Then sommerfelds elementary quantum mechanical theory of metals is discussed. Bibliographical footnotes accessrestricteditem true. This theory is called quantum free electron theory. Classical theory this chapter deals with the classical theory of free electrons in metals developed by lorentz and drude. The classical free electron theory of metals drude lorentz theory of metals postulates.
Metals drudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. Classical theory states that all the free electrons will absorb energy, but quantum theory states only few electrons will absorb energy. 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. What are the merits of classical free electron theory. Quantum free electron theory could successfully explain the electronic sp. N atoms each give one valence electron and the electrons are freely mobile. This textbook focuses on the fully classical theory of fels with application to fel oscillators and develops the fundamentals of fel theory in sufficient depth to provide both a solid understanding of fel physics and a solid background for research in the field. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals. Given its simplicity, it is surprisingly successful in. Chapter 6 free electron fermi gas national tsing hua.
Quantum free electron theory was proposed by arnold sommerfeld. 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. Srit unit iii free electron theory applied physics. The theory of the classical electron presented here is a reformulation of the traditional theory based on a simple application of the causality principle. 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. Find materials for this course in the pages linked along the left.
Describe the classical free electron model of metals in terms of the concept electron number density. 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. Analytical equations to generate the free electron current vector field and the angular momentum density function see app. Classical free electron theory could not explain many physical properties. The valence electrons are treated as though they constitute an ideal gas. To describe the quantum properties of any physical system, a new mathematical language is required as compared to that of classical mechanics. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. Engineering physics ii unit 1 conducting materials. 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. In 1998 he joined the faculty of the university of hawaii where he is currently an associate professor of physics. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. For the love of physics walter lewin may 16, 2011 duration. In solidstate physics, the free electron model is a simple model for the behaviour of charge.
A metal is imagined as the structure of 3dimensional array of ions in between. Hence, classical free electron fails to explain the temperature dependence of electrical conductivity. It is free to move throughout the volume of the metal. Internet archive contributor internet archive language english. B m s institute of technology classical free electron theory. Modeling the analytical equations to generate the atomic orbital currentvector field see ch. According to this theory, the free electrons obey quantum laws. When the field is zero, this equation, obviously, describes the decay of any gross charge carrier motion in any particular direction. 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. Hence classical free electron theory is known as drudelorentz theory. The classical theory had several conspicuous successes, notably the. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. The valence electrons can move freely throughout the body of the solid. 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.
The main assumptions of classical free electron theory are. Department of physics question bank engineering physics ii. Dec 03, 2012 for the love of physics walter lewin may 16, 2011 duration. Engineering physics ii unit 1 conducting materials notes. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. Nov 05, 2016 quantum free electron theory could successfully explain the electronic sp. Mar, 2017 start free trial sign in engineering physics by s. Give the assumptions of the classical free electron theory. Free electron theory of metals request pdf researchgate. What links here related changes upload file special pages permanent link. Chapter 1 transport properties university of virginia.
The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. At its heart quantum mechanics is a mathematically abstract subject expressed in terms of the language of complex linear vector spaces in other words, linear algebra. Causality is the generator of the vacuum gaugea powerful relativistic theory of potentials well suited to resolve fundamental difficulties associated with the classical electron including. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. Heat capacity of metalheat capacity of ion lattice.
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