Drudes theory treated the electrons as an ordinary classical gas. Drude model conductivity frequency dependence plasma. Then sommerfelds elementary quantum mechanical theory of metals is discussed. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. The valence electrons are treated as though they constitute an ideal gas. Classical free electron theory could not explain many physical properties. The free electron theory of metals the evolution of the free electron. Chapter 5 the drude theory of metals delaware physics. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with. 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 model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i.
These free electrons are, therefore, also referred to as free electron gas and the theory is accordingly named as free electron gas model. Some appreciation of the term of relaxation time dt. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. This theory was proposed by making small changes in the classical free electron theory and by retaining most of the postulates of the. Mod01 lec10 the free electron theory of metals electrical conductivity duration. Give the assumptions of the classical free electron theory. Theory of free electrons in metals elefterios lidorikis room. Quantum theory macro particle classical physics based on newtons laws micro particle quantum physics.
The alkali metals are expected to have the best agreement with the free electron model since these metals only one selectron outside a closed shell. Freeelectron theory of metals article about freeelectron. 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.
The classical free electron theory was introduced by p. B m s institute of technology classical free electron theory. The behaviour of free electrons moving inside the metals is considered to be similar to that of atoms or molecules in perfect gas. The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals.
The free electron gas, however, differs from an ordinary gas in some respects. The treatment of a metal as containing a gas of electrons completely free to move within it. The model can be very predictive when applied to alkali and noble metals. According to this free electron in a metal valence electron move randdomly at room. Free electrons in a metal resemble molecules of a gas. Mar, 2017 start free trial sign in engineering physics by s. 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 simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. Classical free electron theory is modeled by drude lorentz to explian elctrical conductivity in metals. This theory is called quantum free electron theory. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals.
Classical drude theory of metals successes and limitations of the classical model. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals. 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. Quantum free electron theory of metals science key. According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. Engineering physics ii unit 1 conducting materials. Srit unit iii free electron theory applied physics. Classical theory states that all free electrons absorb the supplied energy. But quantum theory states that only a few electron absorb the supplied energy. The free electrons, considered identical to the outermost, or valence, electrons of free metal atoms, are presumed to be moving independently of one another. Sommerfeld 1928 applied the principles of quantum mechanics to classical free electron theory. Assumptions or salient features in classical free electron theory the classical free electron theory is based on the following postulates. 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.
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 following assumptions apply to both the theories. This model makes several key assumptions some of which are better approximations than others. This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. According to classical free electron theory the specific heat of metals is given by 4. Put free electrons into a very wide potential well the same size as. 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. The uniqueness in such a type of bonding fashion lies in the fact that unlike ionic bonding and covalent bonding where the sharing of electrons is between two atoms and the electrons remain localized, in metallic bonding the bond is formed among all the atoms in the. Wiedemannfranz law relationship between thermal conductivity k and electron conductivity s. Chapter 6 free electron fermi gas national tsing hua. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. Explain the quantum freeelectron model of metals in terms of paulis exclusion principle calculate the energy levels and energylevel spacing of a free electron in a metal metals, such as copper and aluminum, are held together by bonds that are very different from those of molecules.
Classical free electron theory of metals engineering. So it leads to much larger predicted quantities than that is actually observed. Theory of free electrons in metals university of ioannina. The metals form a unique type of bonding known as metallic bonding and form the lattice structure. L and a are, respectively the length and crosssectional area of the metal. Unit1 classical free electron theory physics youtube. Free electron theory of metals request pdf researchgate. Sommerfelds free electron theory of metals physics assignment. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. The uniqueness in such a type of bonding fashion lies in the fact that unlike ionic bonding and covalent bonding where the sharing of electrons is between two atoms and the electrons remain localized, in metallic bonding the bond is formed among all the atoms in the lattice and the free electrons. Classical free electron theory electrical conductivity.
Electrons in a metal behave much like particles in an ideal gas no coulombic interaction and no. Apr 10, 20 the classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. 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. 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. He realised the role played by pauli exclusion principle in restricting the. Hence, classical free electron fails to explain the temperature dependence of electrical conductivity. 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. In solidstate physics, the free electron model is a simple model for the behaviour of. Classical free electron theory permits all electrons to gain energy. Dec 03, 2012 for the love of physics walter lewin may 16, 2011 duration. Classical derivation of ohms law and drude conductivity. Free electron theory of metals conductivity electrical. Comparison classical free electron theory and quantum free electron theory.
Metals are good conductors both electrical and thermal. Mar 18, 2018 classical free electron theory of metals. Free electron theory of metals nicholas research group. For the love of physics walter lewin may 16, 2011 duration. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the. The free electrons, considered identical to the outermost, or valence. 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. Quantum free electron theory was proposed by arnold sommerfeld. Engineering physics ii unit 1 conducting materials notes.
Notes on the drude model assumptions of the drude model the drude model provides a classical mechanics approach to describing conductivity in metals. 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. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. The electrical conductivity of semiconductor and insulator cannot be explained by this theory. Classical free electron theory of metals this theory was developed by drude and lorentz and hence is also known as drudelorentz theory. The threedimensional thermal conduction in metals j q is the thermal current density, k is the thermal. This theory was developed by drude and lorentz during 1900 all the atoms are composed of and hence is also known as drudelorentz theory. The main assumptions of classical free electron theory are. Quantum free electron theory the failure of classical free electron theory paved this way for quantum free electron theory.
Write down the drawbacks of classical free electron theory. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. Sommerfelds free electron theory of metals physics. Classical free electron theory of metals in order to explain electrical conductivity in metals, lorentz and drude put forward a theory called free electron theory of metals. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. Metalsdrudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. You can download free classical free electron theory of metals engineering physics edurev notes pdf from edurev by using search above. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. The drude theory of metals the model free electron densities densityof the electron gas. Classical free electron theory of metals engineering physics. The classical theory had several conspicuous successes, notably the. Ravindran, phy075 condensed matter physics, spring 20 16 july. Atomic selectrons are delocalised due to overlap of outer orbits.
However even sodium, which is considered to be the closest to a free electron metal, is determined to have a. As per the classical free electron theory, free electrons in a metal are expected to behave just as gas molecules. 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. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. But according to quantum theory, the free electrons occupy different energy levels, up to fermi level at 0 k. The valence electrons can move freely throughout the body of the solid. Quantum free electron theory could successfully explain the electronic sp. Freeelectron theory of metals accessscience from mcgraw. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. 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. Classical free electron gas classical free electron gas ohmic law vvoltage, icurrent, rresistance, rresistivity, sconductivity, and eelectric field.