Effect of impurity and temperature on electrical resistivity of metals. It is incapable of explaining why some crystals have metallic properties and others do not have. The electrons travel with a constant potential inside the metal but confined within its boundaries. Metal that contains free electrons wondering around positive cores. Different phases of the electron liquid, from the landau fermi liquid to the wigner crystal, from the luttinger liquid to the quantum hall liquid are extensively discussed. B m s institute of technology classical free electron theory. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. Apr 01, 2018 drude theory of conduction basics of free electron theory and electrical conductivity part 1 duration. 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. Sommerfield model for free electron theory 9 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. The behaviour of free electrons moving inside the metals is considered to be similar to that of atoms or molecules in perfect gas. Apr 10, 20 the classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates.
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. 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. Some appreciation of the term of relaxation time dt. Ravindran, phy075 condensed matter physics, spring 20 16 july. The drawbacks of quantum free electron theory are as follows. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory.
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 quantum free electron theory somerfield developed this theory in 1928. 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. Free electron theory of metals nicholas research group. This is totally inexplicable within the free electron model. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university does not say anything about the electron energy distribution in metalsare all electrons moving around with about the same energy. It is possible that many electron may possess same energy. According to this theory, the metals containing free electrons obey the laws of classical mechanics.
What are the drawbacks of classical free electron theory. Classical derivation of ohms law and drude conductivity. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. Kronig penny model according to quantum free electron theory of metals, a conduction electron in a metal experiences constant or zero potential and free to move inside the crystal but will not come out of the metal because an infinite potential exists at the surface.
The classical free electron theory drude and lorentz proposed this theory in 1900. 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. Electron gas history electron gas model predates quantum mechanics electrons discovered in 1897 drudelorentz model 1905electrons classical particles free to move in a box model. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. Ravindran, sommerfield model for free electron theory uio. The model can be very predictive when applied to alkali and noble metals. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. Sommerfield model for free electron theory 9 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. Put free electrons into a very wide potential well the. This theory gives the correct mathematical expression for the thermal conductivity of metals.
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. Sommerfelds free electron theory of metals physics assignment. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. 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. This document is highly rated by engineering mathematics students and has been viewed 800 times. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in selection from engineering physics book. Srit unit iii free electron theory engineering physics. According to the classical free electron theory the value of specific heat of metals. Nov 05, 2016 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.
Then sommerfelds elementary quantum mechanical theory of metals is discussed. It could not explain the negative temperature coefficient of resistivity for certain solids 2. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university does not say anything about the electron energy distribution in metals are all electrons moving around with about the same energy. This page contains materials for the session on the band theory of solids. It is pointed out that the current theory of the quantum size effects qse assumes effectively free conduction electrons, and that this assumption is not obviously valid in this qse regime. This theory explains the specific heat capacity of materials. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. Pauli showed that in order to calculate the paramagnetism of free electrons in metals.
It features a 1hour lecture video, and also presents the prerequisites, learning objectives, reading assignment, lecture slides, homework with solutions, and resources for further study. The new quantum mechanics, when applied to the problem of the structure of the atom with pointcharge electrons, does not give results in agreement with experiment. So it leads to much larger predicted quantities than that is actually observed. A natural step was to formulate a quantum theory of electrons in metals. The discrepancies consist of duplexity phenomena, the observed number of stationary states for an electron in an atom being twice the number given by the theory. Jan 20, 2020 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. Sommerfelds free electron theory of metals physics. Drude theory of conduction basics of free electron theory and electrical conductivity part 1 duration. Drude model fails to predict hall and conductivity for all metals except for alkaline metals. What are the drawbacks of quantum free electron theory.
The metals form a unique type of bonding known as metallic bonding and form the lattice structure. Drude theory of conduction basics of free electron theory. But same model predicted that all electrons contribute to heat capacity. This theory is called quantum free electron theory. Apr 19, 2019 free electron theory of conductor was proposed by p. 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. Handout 2 sommerfeld model for metals free fermion gas. Quantum theory of free electron sommerfield theory duration. Quantum free electron theory was proposed by arnold sommerfeld.
Freeelectron theory of metals accessscience from mcgraw. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. Free electron theory of metals conductivity electrical. Pdf free electron theory 201516 vtu shashank mohan. The treatment of a metal as containing a gas of electrons completely free to move within it. Quantum free electron theory of metals science key. Freeelectron theory of metals article about freeelectron. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. Ii, iii, and iv, to the test areas of transport phenomena resulting in band theory, magnetism, and superconductivity. The free electrons, which constitute the electron gas can have continuous energy values. His approach is based upon quantization of electrical energy levels. 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.
Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. In solidstate physics, the free electron model is a simple model for the behaviour of. 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. Quantum size effect and features of nanotechnology materials duration. According to the classical free electron theory the value of specific heat of metals is given by 4. Classical free electron theory permits all electrons to gain energy. It fails to explain why the atomic arrays in crystals including metals should prefer certain structures and not others. 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.
The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. Free electron theory of conductor was proposed by p. Sommerfeld 1928 applied the principles of quantum mechanics to classical free electron theory. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university does not say anything about the electron energy distribution in metals are all electrons moving around with about the same.
The new quantum mechanics, when applied to the problem of the structure of the atom with pointcharge electrons, does not give results in. Mod01 lec10 the free electron theory of metals electrical conductivity duration. Give the assumptions of the classical free electron theory. The development of the quantummechanical electron theory of.
In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. This theory explains photo electric effect, compton effect and block body radiation. The development of the quantummechanical electron theory of metals. 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. Atomic selectrons are delocalised due to overlap of outer orbits.
This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. 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. In solidstate physics, the nearly free electron model or nfe model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. Whereas electrons are quantum particles which obey electrons are known as. The model enables understanding and calculating the electronic band structure of especially metals. All due to the free electrons of the metallic bond outline classical drude theory of metals successes and limitations of the classical model sommerfeld theory of metals quantum statistics and semi. The model is closely related to the more conceptual empty lattice approximation. The free electrons, considered identical to the outermost, or valence. But quantum free electron theory permits only a fraction of electrons to gain energy.
The quantum theory of the electron proceedings of the. Quantum theory of the electron liquid by gabriele giuliani. Quantum free electron theory engineering mathematics notes. Topics include heisenbergs uncertainty principle, normalization, stationary states, wave and group velocities, mean values, and variational method. According to this theory the free electrons obey quantum laws. The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals. These free electrons are, therefore, also referred to as free electron gas and the theory is accordingly named as free electron gas model. The energy values of the free electrons are discontinuous because of which the energy levels are discrete. 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. Both static and timedependent density functional theory are presented in detail. The main assumptions of classical free electron theory are. The book first discusses revision of quantum mechanics. This document is highly rated by electronics and communication engineering ece students and has been viewed 1436 times.
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