Band theory this is a quantummechanical treatment of bonding in solids, especially metals and semiconductors. Handout 2 sommerfeld model for metals free fermion gas. Sommerfelds free electron theory of metals physics assignment. This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. Thermal properties of the free 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 27 48. The electrons, however, are treated using quantum mechanics. Ph8252 physics for information science syllabus notes. Jun 14, 2001 the electron theory of metals describes how electrons are responsible for the bonding of metals and subsequent physical, chemical and transport properties. This is totally inexplicable within the free electron model.
Introduction to the electron theory of metals uichiro. About that time, geometrical terms such as extremal sections, curvatures, diameters, limiting points began to appear in papers on the 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. 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 quantum numbers describe the allowable states electrons may. Quantum theory of the electron liquid modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known. First, the role of the electron pair remains unexplained but appears to be the hinge of both lewiss theory and the vsepr theory. According to quantum free electron theory, both experimental. The triumph and limitations of quantum field 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.
Philip ball will talk about what quantum theory really means and. His approach is based upon quantization of electrical energy levels. Electron theory of metals and geometry rutgers physics. Free electron gas in two dimensions and in one dimension density of states in kspace and in energy in lower dimensions. The development of the quantum mechanical electron theory of metals. Consider the drude formula 1, originally proposed on classical grounds, for the. It did not apply to metals with closed fermi surfaces, i. It explains the free electrons in lattice it obeys the laws of classical mechanics. These electrons can now be put in a quantum superposition of. But quantum free electron theory permits only a fraction of electrons to gain energy. 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.
B m s institute of technology classical free electron theory. Two of the rules of quantum theory that are most important to explaining the atom are the idea of waveparticle duality and the exclusion principle. Pdf we trace the fundamental developments and events, in their. According to the classical free electron theory the value of specific heat of metals is given by 4. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. 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. Why everything you thought you knew about quantum physics is different with philip ball. In this chapter, some of the basic formulas 17 of transport theory are. The development of the quantummechanical electron theory. 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.
The free electrons, considered identical to the outermost, or valence. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. Expressions obtained will be useful when considering real conductors i free electrons. Pdf free electron theory 201516 vtu shashank mohan. It is a microscopic theory, proposed by sommerfeld in 1928. The local relation assumed by maxwell holds when the mean electron free path. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. This theory explains photo electric effect, compton effect and block body radiation.
This theory gives the correct mathematical expression for the thermal conductivity of metals. The treatment of a metal as containing a gas of electrons completely free to move within it. This document is highly rated by electronics and communication engineering ece students and has been viewed 1436 times. Assumptions we will first consider a gas of free classical electrons subject to external electric and magnetic fields. Srit unit iii free electron theory engineering physics. Chapter 27 early quantum theory and models of the atom. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. If an xray photon is scattered by an electron, does the photons wavelength change. The metals form a unique type of bonding known as metallic bonding and form the lattice structure. Nearly massless dirac fermions and strong zeeman splitting in.
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. Classical free electron theory of metals this theory was developed by drude and lorentz and hence is also known as drudelorentz theory. Ph6251 phy2 notes, engineering physics 2 lecture notes. This theory successfully explains electrical conductivity, specific heat. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in selection from engineering physics book. The development of the quantummechanical electron theory of metals.
The classical free electron theory drude and lorentz proposed this theory in 1900. The quantum free electron theory somerfield developed this theory in 1928. 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. Chapter 6 free electron fermi gas national tsing hua. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. The model can be very predictive when applied to alkali and noble 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. The relationship between theory and potential applications is also emphasized. It could not explain the negative temperature coefficient of resistivity for certain solids 2. Before getting into the predictions of the free electron model, its worth a few. 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. The main assumptions of classical free electron theory are. As per the classical free electron theory, free electrons in a metal are expected to behave just.
When the band is occupied by valence electrons, it is called a valence band. This is because the electrons are quantum mechanical particles and fermi. The energy values of the free electrons are discontinuous because of which the energy levels are discrete. Some appreciation of the term of relaxation time dt. The development of the quantummechanical electron theory of. Electrons are treated as point like particles, charge fields, and as gas molecules in an electron gas 2. Since most metals have open fermi surfaces, this theory of the linear magnetoresistance was quite satisfactory. 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. Why everything you thought you knew about quantum physics is.
A proper accounting of these anomalies must await the quantum treatment of metals. 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. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. It is possible that many electron may possess same energy. Freeelectron theory of metals accessscience from mcgraw. The preceding discussion has outlined the general approach to covalent bonding and has shown how it is still widely employed for a qualitative understanding of molecules. Freeelectron theory of metals article about freeelectron. The wiggler and the radiation combine to produce a beat wave, which is. Nearly 100 years after faradays pioneering experiments, the quantum theory confirmed that it is indeed electrical forces that are responsible for the structure of molecules. A natural step was to formulate a quantum theory of electrons in metals. He realised the role played by pauli exclusion principle in restricting the energy values of. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. From the classical free electron theory the value of specific heat of metals is given by. Quantum theory of the electrical conductivity of metals in a.
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. Pdf the development of the quantummechanical electron theory. Page 3 mobility of electrons the mobility of electrons is defined as the magnitude of drift velocity acquired by the electron in a unit field. Unit iii free electron theory engineering physics dr. Metal that contains free electrons wondering around positive cores.
Alternatively, from the spinzero method which is frequently used in quantum oscillation studies of organic conductors 55 and hightc cuprates 6163, a similar gfactor g37. Then sommerfelds elementary quantum mechanical theory of metals is discussed. The classical theory had several conspicuous successes, notably the. Drude theory of conduction basics of free electron theory. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium.
The book starts with the basics of one electron band theory and progresses to cover high tc superconductors and quasicrystals. Quantum free electron theory was proposed by arnold sommerfeld. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. 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. Free electrons are much more efficient in transporting heat compared to phonons. 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. According to this theory, the metals containing free electrons obey the laws of classical mechanics.
Unit i electrical properties of materials classical free electron theory expression for electrical conductivity thermal conductivity, expression wiedemannfranz law success and failures electrons in metals particle in a three dimensional box degenerate states fermi dirac statistics density of energy states electron in periodic potential energy bands in. 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. The free electron model the quantum state of an electron is described by the timeindependent. Drude theory of conduction basics of free electron theory and electrical conductivity part 1 duration. According to this theory, the metals containing free electrons obey the.
The free electrons, which constitute the electron gas can have continuous energy values. The electrons follow the fundamental coulombs inverse square law. What is difference between classical theory and quantum. The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals. Thus, quantum statistics are always important for electrons in metals. Ii, iii, and iv, to the test areas of transport phenomena resulting in band theory, magnetism, and superconductivity. Quantum size effect and features of nanotechnology materials duration. According to this theory the free electrons obey quantum laws. 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 paper gives a consistent quantum mechanical theory of the electrical conductivity of metals in magnetic fields. 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. Created by the best teachers and used by over 51,00,000 students. So it leads to much larger predicted quantities than that is actually observed.
This theory explains the specific heat capacity of materials. The free electron theory of metals electrical conductivity. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Princeton university princeton, new jersey february 1, 2008 abstract talk presented at the conference historical and philosophical re. The valance electrons are not affected by theeltlectronion it tiinteraction. Explain the quantum free electron 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. 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. Squid is made by joining two josephsons junction in the loop of a.
Handout 3 free electron gas in 2d and 1d cornell university. Ravindran, sommerfield model for free electron theory uio. The triumph and limitations of quantum field theory david j. 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. 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. A kinetic equation is deduced for the statistical operator with general assumptions on the energy spectrum of electrons, and the limit of the transition to a classical case is analysed. Give the assumptions of the classical free electron theory. Light of 450nm wavelength strikes a metal surface, and a stream of electrons emerges from the metal. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. 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. This theory is called quantum free electron theory. Theory of free electrons in metals elefterios lidorikis room. Ravindran, phy075 condensed matter physics, spring 20 16 july.
This is where drudes free electron model of the metal the same model that explained electrical and thermal conductivity will help us through. Atomic selectrons are delocalised due to overlap of outer orbits. They follow maxwell boltzmanns distribution to eva. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. Modern electron theory of metals abounds in geometric terminology and, by using geometric ideas, provides. Density of conduction electrons in metals 1022 1023 cm3. Ph6251 phy2 notes, engineering physics 2 lecture notes it 2nd sem anna university 0.
Sommerfeld theory of metals quantum statistics and semi. But same model predicted that all electrons contribute to heat capacity. Sommerfelds free electron theory of metals physics. Drudes theory treated the electrons as an ordinary classical gas. According to this theory, the free electrons obey quantum laws. Effect of impurity and temperature on electrical resistivity of metals. Quantum theory and atomic structure nuclear atom small, heavy, positive nucleus surrounded by a negative electron cloud electronic structure arrangement of the electrons around the nucleus classical mechanics fails in describing the electronic motion quantum mechanics designed to describe the motion of microscopic. Chapter 2 quantum theory introduction quantum theory explains our world at the atomic and molecular levels. 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. In classical free electron theory, proposed by drude and later developed. Quantum free electron theory of metals science key.
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