The classical theory had several conspicuous successes, notably the. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. Hence, classical free electron fails to explain the temperature dependence of electrical conductivity. 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. Some appreciation of the term of relaxation time dt.
Dec 03, 2012 for the love of physics walter lewin may 16, 2011 duration. 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. The theory of the classical electron presented here is a reformulation of the traditional theory based on a simple application of the causality principle. What links here related changes upload file special pages permanent link. These free electrons move freely throughout the lattice and hence are termed as electron gas. Quantum free electron theory could successfully explain the electronic sp. Mar, 2017 start free trial sign in engineering physics by s. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. Before studying the statistical formulation, we will discuss electron dynamics in a perfect crystal. Engineering physics ii unit 1 conducting materials. Mention the drawbacks of classical free electron theory of metals. Given its simplicity, it is surprisingly successful in.
It is free to move throughout the volume of the metal. The valence electrons are treated as though they constitute an ideal gas. Classical free electron theory could not explain many physical properties. For the love of physics walter lewin may 16, 2011 duration. Sommerfelds free electron theory of metals physics assignment. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. According to this theory, the free electrons obey quantum laws. In solidstate physics, the free electron model is a simple model for the behaviour of. 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. When the field is zero, this equation, obviously, describes the decay of any gross charge carrier motion in any particular direction. 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. In 1998 he joined the faculty of the university of hawaii where he is currently an associate professor of physics.
Classical theory this chapter deals with the classical theory of free electrons in metals developed by lorentz and drude. This theory is called quantum free electron theory. Give the assumptions of the classical free electron theory. Put free electrons into a very wide potential well the same size as. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. 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.
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. N atoms each give one valence electron and the electrons are freely mobile. What are the merits of classical free electron theory. The valence electrons can move freely throughout the body of the 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. Bibliographical footnotes accessrestricteditem true. According to this theory, the metals containing free electrons obey the laws of classical mechanics. His current research interests include the theory and design of novel optical resonators for highresolution free electron laser spectroscopy, xray generation and highfield physics. Molar specific heat hence, thermal conductivity k c v th.
The electron has a mass that is approximately 11836 that of the proton. Find materials for this course in the pages linked along the left. In solidstate physics, the free electron model is a simple model for the behaviour of charge. This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. The classical free electron theory was introduced by p. Classical theory of freeelectron lasers book iopscience. 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. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. The classical free electron theory of metals drude lorentz theory of metals postulates. Free electron theory of metals request pdf researchgate.
But quantum free electron theory permits only a fraction of electrons to gain energy. Modeling the analytical equations to generate the atomic orbital currentvector field see ch. Then sommerfelds elementary quantum mechanical theory of metals is discussed. 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. Srit unit iii free electron theory applied physics.
The valence electrons of atoms are free to move about the whole volume of the metals like the. These electrons behaves like classical particles generally we call it electron gas. Apr 10, 20 the classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. A metal is imagined as the structure of 3dimensional array of ions in between. B m s institute of technology classical free electron theory. The main assumptions of classical free electron theory are. Energy of a free electron, for an electron density n specific heat.
Chapter 1 transport properties university of virginia. 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. Landaus model is now known as the fermi liquid theory. To describe the quantum properties of any physical system, a new mathematical language is required as compared to that of classical mechanics. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. Heat capacity of metalheat capacity of ion lattice. Quantum free electron theory of metals science key. 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. 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. Free electron theory of metals nicholas research group.
The collection of valence electrons from all the atoms in a given piece of metal forms electron gas. 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. This in turn will affect the way the electron gas can absorb energy from an external source. Chapter 6 free electron fermi gas national tsing hua. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. Drudes theory treated the electrons as an ordinary classical gas. This theory cannot explain the compton, photoelectric effect, paramagnetism, ferromagnetism, etc. Department of physics question bank engineering physics ii.
The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. Classical free electron theory permits all electrons to gain energy. Classical theory states that all the free electrons will absorb energy, but quantum theory states only few electrons will absorb energy. Energy of the electron is determined by the temperature of metal. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. Comparison classical free electron theory and quantum free electron theory. Heat capacity of the electron gas classical statistical mechanics a free particle should have 3kb2. Hence classical free electron theory is known as drudelorentz theory. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. Internet archive contributor internet archive language english. 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. The electrons dont interact with each other rather with the much larger atomic cores. 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. Quantum free electron theory was proposed by arnold sommerfeld.
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. All due to the free electrons of the metallic bond. 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. The classical free electron theory is based on the following postulates. Nov 05, 2016 quantum free electron theory could successfully explain the electronic sp. Atomic selectrons are delocalised due to overlap of outer orbits. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals.
The free electron model considers that metals are composed of a quantum electron gas. The following assumptions apply to both the theories. 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. Engineering physics ii unit 1 conducting materials notes. Unit1 classical free electron theory physics youtube. Describe the classical free electron model of metals in terms of the concept electron number density.
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