Created by the best teachers and used by over 51,00,000 students. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Free electron theory of solids march 29, 2015 december 30, 2010 by mini physics electrons can be visualised as rattling around insde the metal, randomly changing direction when they collide with positive ions, much like a ball in a pinball machine. Mod01 lec9 the free electron theory of metals youtube. The valence electrons of metallic atoms are free to move about the whole volume of the metals like the molecules of a gas in a container. The electron theory states that since electrons are negatively charged, current flows from the most negative to the most positive point within an electrical circuit.
When the field is zero, this equation, obviously, describes the decay of any gross charge carrier motion in any particular direction. Nearly free electron approximation and tight binding. Lecture notes theory of solids i physics mit opencourseware. Apr 10, 20 the phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. Sommerfelds free electron theory of metals physics. Jun 02, 2015 free electron model in solidstate physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of a metall slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If 0, we assume the electron to be traveling in a weak potential, and can thus expand the wave function into two parts. 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 failure of the free electron theory of metals physics. Dec 09, 20 these four statements represent the general fundamental hypotheses of the theory of electrons. His current research interests include the theory and design of novel optical resonators for highresolution free electron laser spectroscopy, xray generation and highfield physics. Free electron model in solidstate physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of a metallic solid. These free electrons move freely throughout the lattice and hence are termed as electron gas. Then sommerfelds elementary quantum mechanical theory of metals is discussed.
Freeelectron theory of metals article about freeelectron. 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. The electronic structure of surfaces has become a very active area of research in the. Drude attributed the electrons bouncing off the impenetrable ion. Electricity can be defined, then, as charged matter.
The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. Electron theory article about electron theory by the. A statistical equation for describing the mean drift velocity in the direction of the field may be written. Another current flow theory is called the conventional theory. Within the nearly free electron model we start from the dispersion relation of free electrons and analyze the effect of introducing a weak lattice potential. Obtain an expression for the fermi wavevector and the fermi energy for a gas of electrons at absolute zero. The free electron model calculation of the lorenz factor is about twice the value of drudes and its closer to the experimental value. 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. Free electron theory, thermal motion, drift motion, drift velocity, conductivity, mobility, numericals, and other topics. Electron theory states all matter is comprised of molecules, which in turn are comprised of atoms, which are again comprised of protons, neutrons and electrons. The electron theory, which is now accepted and used to explain the behavior of electricity, states that electric current consists of electronflow and can be defined as a moving charge. The electron has a mass that is approximately 11836 that of the proton.
The fundamental hypotheses of the theory of electrons. Note, however, that although the free electron wave vector is simply p, where p is the momentum of the electron, in the bloch case k is not proportional to the. It is free to move throughout the volume of the metal. Transition metals, such as iron, have partially filled electronic d states and are not treated by.
The collection of valence electrons from all the atoms in a given piece of metal forms electron gas. Overlap and bonding however, if atoms get too close, the internuclear repulsion greatly raises the energy. The main assumptions of quantum free electron theory are, the energy levels of the conduction electrons are quantised. Transition metals, such as iron, have partially filled electronic d states and are not treated by the free electron model. Because it was unable to answer why the mean free path of electrons reaches 20nm in a good conducting metal like silver in room tempereture. Jun 15, 2018 these free electrons move freely throughout the lattice and hence are termed as electron gas. There is one electron for every proton in the nucleus, which keeps the atom electrically neutral, as electrons are considered to have a negative charge and protons a positive charge. Also according to this theory the value of electronic specific heat is equal to 32 r. Mar 29, 2015 free electron theory of solids march 29, 2015 december 30, 2010 by mini physics electrons can be visualised as rattling around insde the metal, randomly changing direction when they collide with positive ions, much like a ball in a pinball machine. In solidstate physics, the free electron model is a simple model for the behaviour of. Because an electron, even though smaller than the smallest known. Treating the nearly free electron model using degenerate perturbation theory has been shown on the blackboard during lectures 3. In the lectures we have derived two simple rules, which are away from brillouinzone boundaries the electronic bands i. 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.
Electron theory synonyms, electron theory pronunciation, electron theory translation, english dictionary definition of electron theory. With this heat capacity the free electron model is also able to predict the right order of magnitude and temperature dependence at low t for the seebeck coefficient of the thermoelectric effect. According to the classical free electron theory the value of specific heat of metals is given by 4. What links here related changes upload file special pages permanent link page. Electronic heat capacity has an additional temperature dependent contribution from the electrons. Every investigation based on them, and only such one, is to be denoted as belonging to the framework of the theory of electrons. The third period was a period of striving to understand and finally accept the wave and spin properties of the electron through formulating wave mechanics and relativistic quantum theory of the electron.
The nearly free electron model is a modification of the freeelectron gas model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a crystalline solid. This theory is widely accepted by the electronic industry. This model, like the free electron model, does not take into account electron electron interactions. This gives rise to the nearlyfree electron model the electrons can now interact with the periodic latttice physical picture nearly free electrons. As we shall see, this removes many thermal anomalies of the drude model. Electron pair can be shared when halffilled orbital of one atom overlaps with halffilled orbital of another. In solidstate physics, the free electron model is a simple model for the behaviour of charge. Pauli exclusion principle, fermi statistics simplest model for. This period finished with the establishment of quantum. Electron theory definition of electron theory by the free.
Electronic structure 103 in the following chapter, we will also learn some experimental techniques that are currently used to investigate the electronic properties of the bulk and the surface. The maxwellhertz equations hold in space devoid of matter and electricity. Electron theory definition of electron theory by the. 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. According to the classical free electron theory the value of specific heat of metals is. Classical theory of freeelectron lasers book iopscience. The freeelectron model cannot explain why some elements are metals and others insulators.
In the nearly free electron model, we take the opposite approach. Chapter 4 electronic structure the electronic properties of matter determines its macroscopic behavior. In other words, current flows from negative to positive. The free electron approximation remains a good approximation well away from the edges of the brillouin zone only wavevectors close to a multiple of. Freeelectron theory of metals accessscience from mcgraw. Electron theory article about electron theory by the free. Some appreciation of the term of relaxation time dt. Show that the density of states at the fermi surface, dndef, can be written as 3n2ef. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. In 1998 he joined the faculty of the university of hawaii where he is currently an associate professor of physics. An example is given below for a nearly free electron model. The first page of the pdf of this article appears below.
Pauli exclusion principle, fermi statistics simplest model for metals. Free electron theory of solids mini physics learn physics. This model, like the freeelectron model, does not take into account electronelectron interactions. Atomic selectrons are delocalised due to overlap of outer orbits. Sep 25, 2017 this lecture talks about free electron theory. Energy bands nearly free electron model electron diffraction and energy gap bloch theorem the central equation emptylattice approximation tightbinding model see chap 9 nfe model is good for na, k, al etc, in which the lattice potential is only a small perturbation to the electron sea. The distribution of electrons in various allowed energy levels occur as per pauli exclusion principle. Recall nature of free electron gas free electrons in box of size l x l x l artificial but useful solved schrodinger equation states classified by k with ek h 22m k periodic boundary conditions convenient. The treatment of a metal as containing a gas of electrons completely free to move within it. This textbook focuses on the fully classical theory of fels with application to fel oscillators and develops the fundamentals of fel theory in sufficient depth to provide both a solid understanding of fel physics and a solid background for research in the field.
However, the following assumptions of classical electron theory continue to be applicable in quantum free electron theory also. He realised the role played by pauli exclusion principle in restricting the energy values of. The nearly free electron model is a modification of the free electron gas model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a crystalline solid. The new quantum mechanics, when applied to the problem of the structure of the atom with pointcharge electrons, does not give results in. May 20, 2006 why did the free electron theory of metals fail the free electron of model my effort. Explain what is meant by the fermi energy, fermi temperature and the fermi surface of a metal.
A molecule is the smallest part of matter which can exist by itself and contains one or more atoms. One corresponding to a plane wave, or a free electron, and another corresponding to a periodic correction factor. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. Nearly free electron in the tight bonding model, the electron eigenstates are initially assumed to be localized around the atoms, then a hopping term is introduced to allow them to delocalize. That is, the electron eigenstates are initially assumed to. Dec 29, 2015 the electron theory, which is now accepted and used to explain the behavior of electricity, states that electric current consists of electronflow and can be defined as a moving charge. Unit1 classical free electron theory physics youtube.
Sommerfelds free electron theory of metals physics assignment. The theory of electrons, the most promising continuation of maxwell s electrodynamics, is based on the following general presuppositions. They postulate a reference system, in which plane electromagnetic waves are propagating in all directions with the same velocity. Find materials for this course in the pages linked along the left. Basic concepts, energy level splitting and energy bands, conductivity and band structure, conductorsmetals, semi metals, insulators, semiconductors, and. B m s institute of technology classical free electron theory. Increased overlap brings the electrons and nuclei closer together while simultaneously decreasing electron electron repulsion. His approach is based upon quantization of electrical energy levels. The energy e of free electrons which is plotted versus k in fig. The logic is very similar to getting optical and acoustic phonon branches by changing atom masses and thereby reducing the size of the brillouin zone. Tsymbal 4 lattice vector, if the bloch form 14 holds for k, it will also hold for k.
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