Drude sommerfeld model lets compare the modified drude model with experimental measurement p. Many of these errors occur because the electrons velocity and energy are deduced from a classical distribution. Notes on the drude model assumptions of the drude model the drude model provides a classical mechanics approach to describing conductivity in metals. Lecture 6 specific heat of electron gas, transport properties within the sommerfeld model. Consider a metal described by a drude model subjected to an oscillating electric eld. Dielectric function and drude model the dielectric function of a medium, determined by its intrinsic electronic structure, is given by 2,3 d ir,t ijr,r,t,te jr,tdt dr, 1 23572. The drudesommerfeld model and the problem of heat capacity copied from the drudesommerfeld model, to facilitate comments.
When the conductivity is low, namely, when the displacement current is larger than the. Drude optical properties of metals 8 plasma frequency 1 to improve accuracy of drude model, effective number of free electron is usually introduced damping frequency damping frequency scattering time generally correlates with conductivity but not accurately 12 2 0 p 2 qn m z sq h. 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. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. The drudesommerfeld model and the problem of heat capacity. The localization energy can also play a role metal. The drude sommerfeld model and the problem of heat capacity by miles mathis first published june 8, 20 in this paper, we will look at the free electron model or drude sommerfeld model of electron transfer in elements. Lecture 8 lossy media, lorentz force law, and drude. Recognizes that their energies are discrete treats them like a particle in a box of constant energy. With the use of this formula, the expression of the electrical conductivity can be derived for both drude model and sommerfeld model without the use of boltzmann equation.
Sommerfeld himself was nominated 81 times more than any other person but was never awarded the nobel prize. Sommerfeld atomic model this model explains the fine spectrum of hydrogen atom. Understanding of physics on electrical conductivity in metals. To account for these shortcomings sommerfeld in 1927 developed a model for electrons in metals that took into consideration the fermidirac statistics of electrons note added. This idea will have many applications, even beyond the drude model. 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. Classical theory drude model drude model, 1900ad, after thompsons discovery of electrons in 1897 based on the concept of kinetic theory of neutral dilute ideal gas apply to the dense electrons in metals by the free electron gas picture success. Sommerfeld theory replaces f bv of drude s theory with fv profound consequences on and c v daniele to oli january 11, 2017 5 48.
Three years after the discovery of the electron by j. In 1927 sommerfeld applied fermidirac statistics to the drude model of electrons in metals a model put forth by paul drude. Condensed matter physics i problem set i drude model, sommerfeld expansion institute of mathematical sciences, chennai due on 8. 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. Sommerfeld atomic model,the angular momentum of electron. The sommerfeld model provides a good description of free electrons in alkali metals such as potassium, which has a fermi energy of 2. Drude conductivity i current density carried by electrons. Given its simplicity, it is surprisingly successful in. Although i will criticize the model harshly, and ultimately correct and extend it, it is not.
Predictions from the drude model relaxation times and electrons velocities mean electrons velocity, v 0. Sommerfelds free electron theory of metals physics. Jun 10, 2008 as far as i know, free electron model is a combination of the quantum behaviour of electrons pauli principle and the classical drude model. Explain why potassium and most other alkali metals can be described well with the. Metals and insulators measured resistivities range over more than 30 orders of magnitude. To order a physical copy of this catalog, simply click on the add. The important postulates of sommerfeld atomic model are1 the orbits may be both circular or elliptical. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. This is usually just known as the drude model or the.
Notes on the drude model assumptions of the drude model. Chapter 6 free electron fermi gas national tsing hua. This happens for radio wave propagating in the saline solution of the ocean, the earth, or wave propagating in highly conductive metal, like your induction cooker. Handout 1 the drude and sommerfeld models of metals this series of lecture notes covers all the material that i will present via transparencies during this. Drude model conductivity frequency dependence plasma. Jan 30, 2020 in the drude model, all electrons contribute to the conductivity, with the scattering with the same relaxa tion time.
The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. Sommerfelds free electron theory of metals physics assignment. In this paper, we will look at the drudesommerfeld model of electron transfer in elements. Lorenz model harmonic oscillator model without restoration force that is, free electrons which are not bound to a particular nucleus linear dielectric response of matter. The kubo formula for the electrical conductivity will be also discussed. Sommerfeld sommerfeld theory of metals keep most assumptions in drude drude model. This is due to overestimation of by about a factor of 100 as we shall when we study the sommerfeld model. Listen to the audio pronunciation of drude sommerfeld model on pronouncekiwi. The new theory solved many of the problems predicting thermal properties the original model had and became known as the drudesommerfeld model. In the drude model, all electrons contribute to the conductivity, with the scattering with the same relaxa tion time.
Using this expression, we ge t an unrealistically small drift velocity. Ravindran, phy075 condensed matter physics, spring 20 16 july. Further, for ee f, the probability value falls off to zero rapidly figure 11. Thank you for helping build the largest language community on the internet. Handout 2 sommerfeld model for metals free fermion gas. I think you will be hard pressed to find a better short summary than chapter 3. An electron experiences a collision, and then, after a time t, a second collision. His approach is based upon quantization of electrical energy levels. The crucial idea was that a spectral line is made up of coinciding. Although i will criticize the model harshly, and ultimately correct and extend it. Conduction current in metalsconduction current in metals 2 2.
The fermi energy is the most probable, or the average energy of the electron across which the energy transitions occurs at temperature above zero degree absolute, which result in the conductivity of the metal. Drude theory in the calculations above, we didnt consider the electron collisions. In an electric eld f ee, and at steady state dp dt 0, current density j nevwhere nis the electron density and v p m with m being the e ective mass of the electron. Classical mechanics quantum mechanics electrons in metals are. The drude model can be visualised using the following simulation. Pdf understanding of physics on electrical resistivity in. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. Include the drude scattering time into the differential equation for the velocity you formulated in 4. Observed values of q are vk about 100 times too small. Eytan grosfeld drude model, sommerfeld model, tightbinding formalism and second quantization 1.
Electrons in a metal behave much like particles in an ideal gas no coulombic interaction and no. 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. Retains almost all aspects of drude model with the following modifications. He realised the role played by pauli exclusion principle in restricting the energy values of.
Uses pauli principle to distribute them in the available energy states. The smallscale details of the potential due to the ionic cores shown schematically in b are replaced by an average potential v 0. The drude model peter hertel overview model dielectric medium permittivity of metals electrical conductors faraday e ect hall e ect paul drude, german physicist, 18631906. Lecture 8 lossy media, lorentz force law, and drudelorentz. In such a picture, the ionic cores merely maintain. The above discussion on the variation fe with e, brings forth the point that.
If we treat the collisions using the drude approximation assuming that the collisions are described by a single parameter. The above equation 1 is known as the drude electron transport equation. Thermo power 100 times smaller than drude value, closer to measured values of q. Free and independent electrons, but no assumptions about the nature of the scattering. Also sometimes the measured value of q is positive drude model has no answer to this. Orlando february 9, 2004 the source of the binding energy is primarily the electrostatic potential between the nuclei and the electrons. Six of sommerfelds students werner heisenberg, wolfgang pauli, peter debye, hans bethe, linus pauling, and isidor i. 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 electrons bouncing. The pauli principle plays the role of a quantum mechanical. The drude and sommerfeld models of metals in other words, the collisions produce a frictional damping term. Schematic of the electronic potential assumed in the drude and sommerfeld models of metals a. 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.
Lossy media, lorentz force law, and drudelorentzsommerfeld model 75 current, or that. 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. Ganesh the drude model is inadequate in many respects, e. Sommerfeld s extension of bohrs atomic model was motivated by the quest for a theory of the zeeman and stark effects. Predictions from the drude model conductivity from drude model. Pdf how sommerfeld extended bohrs model of the atom. Sommerfield model for free electron theory 19 we set out to do a quantum drude model, and did not explicitly include any direct interactions due to the coulomb force, but we ended up with something very different. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. Thomson in 1897, paul drude developed a model which provides an effective description of the transport and optical properties of solids. Arnold johannes wilhelm sommerfeld, formemrs german. 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. 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 drude sommerfeld model. Understanding of physics on electrical conductivity in.
With no applied field, it can be seen that the electrons move around randomly. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. The drude model is applied mainly to metals, but it is equally applicable to heavily doped semiconductors. Sommerfeld theory replaces f bv of drudes theory with fv.
Click on the left and right arrows of each browser window or scroll your mouse wheel up and down. 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 drude model provides a classical mechanics approach to describing conductivity in metals. Other properties of electron gas from sommerfeld model. Assumptions most are very similar to those of drude. Thus the difference between free electron model and drude, is that fem takes into account that electrons are fermions, hence we get a fermi surface in kspace even at temperature of 0k.
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