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. The free electrons, considered identical to the outermost, or valence. Classical free electron theory permits all electrons to gain energy. Quantum free electron theory was proposed by arnold sommerfeld. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. Classical free electron theory electrical conductivity. 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. Drude model conductivity frequency dependence plasma. Classical theory states that all free electrons absorb the supplied energy. The classical free electron theory of metals drude lorentz theory of metals postulates. B m s institute of technology classical free electron theory. Hence, classical free electron fails to explain the temperature dependence of electrical conductivity. Classical free electron theory is modeled by drude lorentz to explian elctrical conductivity in metals.
These free electrons are, therefore, also referred to as free electron gas and the theory is accordingly named as free electron gas model. Atomic selectrons are delocalised due to overlap of outer orbits. The classical theory had several conspicuous successes, notably the. In solidstate physics, the free electron model is a simple model for the behaviour of. 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. Sommerfeld 1928 applied the principles of quantum mechanics to classical free electron theory. Free electrons in a metal resemble molecules of a gas. Some appreciation of the term of relaxation time dt. His approach is based upon quantization of electrical energy levels. This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. Freeelectron theory of metals article about freeelectron. Unit1 classical free electron theory physics youtube. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with.
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. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. Engineering physics ii unit 1 conducting materials notes. Sommerfelds free electron theory of metals physics assignment. The threedimensional thermal conduction in metals j q is the thermal current density, k is the thermal. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. Free electron theory of metals request pdf researchgate. The treatment of a metal as containing a gas of electrons completely free to move within it. Quantum theory macro particle classical physics based on newtons laws micro particle quantum physics. This theory was proposed by making small changes in the classical free electron theory and by retaining most of the postulates of the. Classical free electron theory of metals engineering. Put free electrons into a very wide potential well the same size as. 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.
Drudes theory treated the electrons as an ordinary classical gas. 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. The main assumptions of classical free electron theory are. This theory was developed by drude and lorentz during 1900 all the atoms are composed of and hence is also known as drudelorentz theory. Theory of free electrons in metals elefterios lidorikis room. Classical derivation of ohms law and drude conductivity. According to classical free electron theory the specific heat of metals is given by 4. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals. Chapter 5 the drude theory of metals delaware physics. The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals. Electrons in a metal behave much like particles in an ideal gas no coulombic interaction and no. However even sodium, which is considered to be the closest to a free electron metal, is determined to have a.
The classical free electron theory was introduced by p. This theory is called quantum free electron theory. 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. 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 free electron theory of metals the evolution of the free electron. In an atom electrons revolue around the nucleus and a metal is composed of such atoms.
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. Sommerfelds free electron theory of metals physics. Quantum free electron theory could successfully explain the electronic sp. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. The valence electrons are treated as though they constitute an ideal gas. But quantum theory states that only a few electron absorb the supplied energy. L and a are, respectively the length and crosssectional area of the metal. So it leads to much larger predicted quantities than that is actually observed. Classical free electron theory of metals engineering physics. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. Metals are good conductors both electrical and thermal. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. Wiedemannfranz law relationship between thermal conductivity k and electron conductivity s. Mar 18, 2018 classical free electron theory of metals.
The free electron gas, however, differs from an ordinary gas in some respects. The free electrons, considered identical to the outermost, or valence, electrons of free metal atoms, are presumed to be moving independently of one another. The valence electrons can move freely throughout the body of the solid. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. Srit unit iii free electron theory applied physics.
Classical drude theory of metals successes and limitations of the classical model. Engineering physics ii unit 1 conducting materials. 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. As per the classical free electron theory, free electrons in a metal are expected to behave just as gas molecules. According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. Mod01 lec10 the free electron theory of metals electrical conductivity duration. The model can be very predictive when applied to alkali and noble metals.
The following assumptions apply to both the theories. Mar, 2017 start free trial sign in engineering physics by s. 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. 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. Then sommerfelds elementary quantum mechanical theory of metals is discussed. You can download free classical free electron theory of metals engineering physics edurev notes pdf from edurev by using search above. 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. Notes on the drude model assumptions of the drude model the drude model provides a classical mechanics approach to describing conductivity in metals. But according to quantum theory, the free electrons occupy different energy levels, up to fermi level at 0 k.
Apr 10, 20 the classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. Free electron theory of metals nicholas research group. Assumptions or salient features in classical free electron theory the classical free electron theory is based on the following postulates. Quantum free electron theory the failure of classical free electron theory paved this way for quantum free electron theory. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. The drude theory of metals the model free electron densities densityof the electron gas. He realised the role played by pauli exclusion principle in restricting the. 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. Dec 03, 2012 for the love of physics walter lewin may 16, 2011 duration. 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. Write down the drawbacks of classical free electron theory.
Ravindran, phy075 condensed matter physics, spring 20 16 july. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. 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. Freeelectron theory of metals accessscience from mcgraw. 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. The behaviour of free electrons moving inside the metals is considered to be similar to that of atoms or molecules in perfect gas. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. 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. According to this free electron in a metal valence electron move randdomly at room. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. Comparison classical free electron theory and quantum free electron theory.
For the love of physics walter lewin may 16, 2011 duration. Give the assumptions of the classical free electron theory. Free electron theory of metals conductivity electrical. Metalsdrudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. 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 model makes several key assumptions some of which are better approximations than others. Theory of free electrons in metals university of ioannina. Classical free electron gas classical free electron gas ohmic law vvoltage, icurrent, rresistance, rresistivity, sconductivity, and eelectric field. Chapter 6 free electron fermi gas national tsing hua. The metals form a unique type of bonding known as metallic bonding and form the lattice structure. Quantum free electron theory of metals science key. Classical free electron theory could not explain many physical properties. The electrical conductivity of semiconductor and insulator cannot be explained by this theory. According to classical free electron the electronic specific heat is equal to r 2 3 while the actual value is 0.