Crystal as infinite well potential electron confined in crystal of size. Throughout the 1910s and well into the 1920s, many problems were attacked using the old quantum theory with mixed results. The pauli exclusion principle requires that the replacement of maxwell boltzmann distribution with the fermi dirac distribution as. Ravindran, sommerfield model for free electron theory uio. Sommerfeld s extension of the bohr theory in 19151916, it was turned into a powerful tool of atomic research and adopted and further developed by german physicists in particular. But same model predicted that all electrons contribute to heat capacity. According to this theory, the free electrons obey quantum laws. According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. The development of the quantummechanical electron theory of. Free classical electrons l consider a gas of free classical electrons moving under the influence of electric and area a magnetic fields. Shortly afterwards, through bohrs fundamental work from 19 onwards rutherfords nuclear model of the atom was linked up with plancks quantum theory of thermal radiation, and rydbergs constant of spectra was reduced to the quantum of action and the charge and mass of the electron with a supplementary correction for the motion of. Effect of impurity and temperature on electrical resistivity of metals. Sommerfelds contributions to quantum theory springerlink.
We can assume that the electron gas is contained in a cubic box of edge l. See your course of solid state physics and am chapter 2. His approach is based upon quantization of electrical energy levels. According to this theory, the metals containing free electrons obey the laws of classical mechanics. 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 solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. 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 treatment of a metal as containing a gas of electrons completely free to move within it. Groundstate properties of the electron gas quantum mechanical solution mathematical treatment. Quantum free electron theory of metals science key. Sommerfeld 1928 applied the principles of quantum mechanics to classical free electron theory.
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. Standard topics such as crystal structure, reciprocal space, free electrons, band theory, phonons, and magnetism are covered. This paper contin ues an earlier study of the first phase of the development. Pdf sommerfeld s extension of bohrs atomic model was motivated by the quest for a theory of the zeeman and stark effects. Known as old quantum theory, it did not represent any coherent theory of general applicability. Quantum theory of fermi gas conductivity electrical. The main assumptions of classical free electron theory are. Basics of free electron theory and electrical conductivity part 1 duration. Low temperature specific heat of the free electron gas. The electrons inside the box are confined in a threedimensional infinite potential well with zero potential inside the box and infinite potential outside the box the electron states inside the box are given by the schrodinger equation. The sommerfeld theory was simply the lorentz theory with the fermidirac distribution function replacing the boltzmannmaxwell distribution function. These free electrons move freely throughout the lattice and hence are termed as electron gas.
Electron theory basic concepts of matter the electron theory, which is now accepted and used to explain the behavior of electricity, states that electric current consists of electron flow and can be defined as a moving charge. The weaknesses of the bohr model could be partially eliminated by the physicist arnold sommerfeld. His many contributions included papers in 1915 and 1916 extending niels bohrs planetary model of the atom beyond circular orbits and his incorporation of relativistic corrections in order to explain hydrogenic fine structure. If any questions please contact me whatsap number 9416939577. The freeelectron model was first proposed by the dutch physicist hendrik a. 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. The periodic potential of nuclei is still neglected. This lecture series constitutes a first undergraduate course in solid state physics delivered in an engaging and entertaining manner by professor steven h. Sommerfeld s model was much closer to the modern quantum mechanical picture than bohrs.
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. Pdf sommerfelds extension of bohrs atomic model was motivated by the quest for a theory of the zeeman and stark effects. In1928, byapplyingquantummechanicalprinciples,arnoldsommerfeld succeededinovercomingmany. Arnold sommerfeld was a famous atomic physicist and mathematician who is known mostly for his work on atomic theory in the field of quantum mechanics and for mentoring more recipients of the nobel. According to sommerfeld, the path of an electron around the nucleus, in general, is an ellipse with the nucleus at one of its foci. Lorentz shortly after 1900 and was refined in 1928 by arnold sommerfeld of germany. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. According to this theory, the free electrons move in a periodic field provided by the lattice. Bohr sommerfeld quantum theory of the magnetic monopoles, electron electromagnetic mass and fine structure constant article pdf available july 2010 with 394 reads how we measure reads. 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. Quantum free electron theory was proposed by arnold sommerfeld. 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. Drude theory of conduction basics of free electron theory. Pdf how sommerfeld extended bohrs model of the atom.
Freeelectron theory of metals article about freeelectron. 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. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. Ravindran, phy075 condensed matter physics, spring 20 16 july. The electrons travel with a constant potential inside the metal but confined within its boundaries. This book, written near the beginning of the century by one of physics true giants, arnold sommerfeld, does what most of the newer books involving fancy graphics and glossy paper dont. The theory would have correctly explained the zeeman effect, except for the issue of electron spin. Sommerfeld free electron theory of electrons in metals. Srit unit iii free electron theory engineering physics. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. Sommerfeld proposed this theory in 1928 retaining the concept of free electrons moving in a uniform potential within the metal as in the classical theory, but treated. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. Treating electrons as free quantum particles fermions.
Given its simplicity, it is surprisingly successful in explaining many experimental phenomena, especially the wiedemannfranz law which relates electrical. 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 attraction between the electrons and the lattice ions and the. The development of the quantummechanical electron theory. Although the model provided a satisfactory explanation for certain properties e. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. According to the bohr sommerfeld quantum theory, electrons move about the nucleus of an atom in welldefined orbits, each of which is characterized by four numbers, called quantum numbers. Ece 407 spring 2009 farhan rana cornell university. No contradiction between sommerfeld s quantum hypothesis and. Handout 2 sommerfeld model for metals free fermion gas.
But quantum free electron theory permits only a fraction of electrons to gain energy. The former two immediate successes of the quantum theory, the latter a persistent failure in this period. Drude model fails to predict hall and conductivity for all metals except for alkaline metals metal li na k ag au al inr h en 0780. Because an electron, even though smaller than the smallest known. Arnold sommerfeld 18681951 was among the most important students of the socalled older quantum 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 theory, but treated the electrons as obeying the laws of quantum mechanics. Relativity and quantum theory from sommerfeld to dirac. How is the different electron configuration reflected in the periodic table. This in turn will affect the way the electron gas can absorb energy from an external source.
Mar, 2017 start free trial sign in engineering physics by s. Sommerfeld6 treated the drude electron gas quantum mechanically. Quantum theory of free electron sommerfield theory 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. Electrons inside the atoms of a solid have wave nature free electrons move throughout the crystal. 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. Through the formative years of quantum theory, from 1900 to about 1928, arguments based on the theory of. It was developed in 1927, principally by arnold sommerfeld, who combined the classical drude model with quantum mechanical fermi dirac statistics and hence it is also known as the drude sommerfeld model. Atomic selectrons are delocalised due to overlap of outer orbits. In solidstate physics, the free electron model is a simple model for the behaviour of. Sommerfelds free electron theory of metals physics assignment. Quantum theory of free electron sommerfield theory. 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. In addition to the allready introduced shells by bohr, sommerfeld further introduced subshells also referred to as orbitals.
Electrons inside the atoms of a solid have wave nature free electrons. The new quantum mechanics, when applied to the problem of the structure of the atom with pointcharge electrons, does not give results in. See your course of solid state physics and am chapter 8. Accelerated atomic electron spiral into nucleus definition. Electricity can be defined, then, as charged matter. Then sommerfelds elementary quantum mechanical theory of metals is discussed. Failures of classical free electron theory gave rise to quantum free electron theory by sommerfield. Apr 01, 2018 quantum theory of free electron sommerfield theory. Sommerfelds free electron theory of metals physics.
Chapter 6 free electron fermi gas national tsing hua. The following assumptions of classical free electron theory holds good in quantum free electron theory also. As there are two quantum states for each energy level pauli exclusion principle, therefore, the density of states number of electronic states per unit energy range of a free electron gas in one dimension is from equation xvi, the above equation reduces to the variation of density of states d e with energy e is shown in fig. Unit iii free electron theory engineering physics dr. Pdf how sommerfeld extended bohrs model of the atom 19. An electron moving in an orbit close to the nucleus has a larger. In the free electron model, there is no lattice, and no electronelectron interaction, but it gives nice. This includes a brief note on sommerfeld s relativistic correction also towards solving the fine structure puzzle. The turn of the twentieth century, of a free electron theory. 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. Probability density given by with boundary conditions used for solution of the sch. This lecture can also be considered as lecture 4 of atomic structure and atomic spectra lecture series.
One is able to specify the position of an electron on a scale small compared with a distance over which the field or temperature varies. Quantum particles in a periodic potential of the nuclei. 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. Sommerfeld introduced quantum mechanical concepts, most notably the pauli exclusion principle. This is totally inexplicable within the free electron model. Ohmsohms lawlaw andand electronelectron driftdrift electric fieldelectric field e drift velocity v d current densitycurrent densityjij ia volume element.
Classical free electron theory permits all electrons to gain energy. 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. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. It was developed in 1927, principally by arnold sommerfeld, who combined the classical drude model with quantum. In 1916 arnold sommerfeld generalized the bohr quantization rule beyond the problem of the one electron atom. The new and more general bohrsommerfeld theory described the atom in terms of two quantum numbers, while bohr had originally used only one quantum number. This theory is called quantum free electron theory. The development of the quantummechanical electron theory of metals. Quantum theory and the special theory of relativity emerged almost simultaneously. Given its simplicity, it is surprisingly successful in explaining many. The quantum state of an electron is described by the.
1082 767 1301 394 977 1472 420 993 1579 622 1624 1681 848 653 154 773 885 78 1181 759 1271 173 1667 215 1030 114 1013 392 1094 388 1144 1338 290 387 780 430 149 168 1446 71 94 1043 1484 276 330 983 526 711