# What is Drude model: Definition and 19 Discussions

The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials (especially metals). 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 and re-bouncing off heavier, relatively immobile positive ions.
The two most significant results of the Drude model are an electronic equation of motion,

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{\displaystyle {\frac {d}{dt}}\langle \mathbf {p} (t)\rangle =q\left(\mathbf {E} +{\frac {\langle \mathbf {p} (t)\rangle \times \mathbf {B} }{m}}\right)-{\frac {\langle \mathbf {p} (t)\rangle }{\tau }},}
and a linear relationship between current density J and electric field E,

J

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{\displaystyle \mathbf {J} =\left({\frac {nq^{2}\tau }{m}}\right)\mathbf {E} .}
Here t is the time, ⟨p⟩ is the average momentum per electron and q, n, m, and τ are respectively the electron charge, number density, mass, and mean free time between ionic collisions. The latter expression is particularly important because it explains in semi-quantitative terms why Ohm's law, one of the most ubiquitous relationships in all of electromagnetism, should hold.The model was extended in 1905 by Hendrik Antoon Lorentz (and hence is also known as the Drude–Lorentz model) to give the relation between the thermal conductivity and the electric conductivity of metals (see Lorenz number), and is a classical model. Later it was supplemented with the results of quantum theory in 1933 by Arnold Sommerfeld and Hans Bethe, leading to the Drude–Sommerfeld model.

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1. ### I Drude model with and without an electric field

Why in the Drude model without e-field no energy is transfer by electrons to ions, but when there is an e-field electrons transfer energy to ions ?
2. ### Relaxation time and average electron velocity in Drude model

If τ is the relaxation time, τ means, on average the time between two collisions for an electron moving under a constant electric field inside a metal. Now according to the assumptions of drude model, the electron acquires an additional velocity of \frac{-eEt}{m}where t is the time elapsed since...
3. ### I Running through a complex math derivation of plasma frequency

Background of problem comes from Drude model of a metal (not necessary to answer my problem but for the curious): Consider a uniform, time-dependent electric field acting on a metal. It can be shown that the conductivity is $$\sigma = \frac{\sigma_0}{1-i\omega t}$$ where \sigma_0 =...
4. ### I Drude Model Permittivity Formula - e^iwt or e^(-iwt)?

I've been having a sign problem while deriving the permittivity formula using Drude model, and I found out that the problem came from the fact that complex field vectors are expressed with e-iwt, not eiwt, thus producing (-iwt) term when differentiated...
5. ### Why is the refractive index for red lower than for blue?

By observing that red is the outermost color of the rainbow it is possible to conclude the refractive index of water, n, is lower for red than for blue. However, why is n lower for red? This seems to be answered by the Drude dispersion model, with a resonance in the ultraviolet region, but I...
6. ### B Does the Drude Model Account for J Cross B Force in Hall Conductivity?

I was thinking about hall conductivity, when this question popped up. If there is a magnetic field and an electric field perpendicular to it, then a hall current is generated since the ions have larger gyro radii compared to electrons. Now this current would produce a J cross B force in the...
7. ### Reworking of the Drude model using scattering statistics

Homework Statement The problem I have been set is to rework the Drude model using clearly defined scattering statistics. Homework Equations The Drude model as we have been given it is in terms of momentum \vec{p}(t+dt)=(1-\frac{dt}{\tau})(\vec{p}(t)-q\vec{E}(t)dt)+(\frac{dt}{\tau})(0) Where...
8. ### Drude model relaxation time approximation

In the Drude model of the free electron gas to explain the conduction of a metal, the relaxation time approximation that the electron has a collision in an infinitesimal time interval ##dt##is ##dt/\tau##. It can be shown that the mean time between collisions is ##tau##. If we choose an...
9. ### Does the Drude model predict the emission of em waves?

The Drude model of electrical conduction has the charge carriers being accelerated by an electric field and then interacting with the lattice ions. The cycle is then repeated. An unbound charged particle if accelerated emits electromagnetic waves. Does that mean that a prediction of the Drude...
10. ### Drude model electron interaction

In every source I've checked so far, we make the assumption that we can neglect electron-electron interaction in this model but they always fail to give any reason to answer why this is plausible. Does anyone know how physicists convinced themselves of this at the time and even now (other than...
11. ### Drude Model: Electrons & Collisions

As far as I understand: In the Drude model we take the electron to be moving in a random direction after each collision (*), such that the mean velocity is simply the average of -eEt/m, which is just -eEτ/m, where τ is the relaxation time. But I am very confused about this basic assumption...
12. ### What is Not Directly Proportional to Current Density in the Drude Model?

Homework Statement In the drude model of electrical conduction, the current density (J) is not directly proportional to : a. The average time interval between sucessive collisions b. the number of charge carriers per unit volume c. The square of the electron charge d. The electric field...
13. ### Momentum probability density change in colisions (Drude Model)

Homework Statement A particle suffers elastic colisions with scattering centers with a probability of colision per unit time \lambda. After a colision the particle is in a direction caracterized by a solid angle d\Omega with probability \omega(\theta) d\Omega, that depends only on the angle...
14. ### Solid State - Sommerfeld Drude Model, Calculating N of Elect.

Hello PF :) Homework Statement Consider a system of N electrons at temperature T = 0, each having a mass of m, confined to volume V. Find the number of electrons that: a) have momentum p<p_f/2 b) ... Homework Equations The relevant equations can be derived below: but here is a...
15. ### Drude model and electron mean free path?

Could someone explain mean free electron paths with regard to; Drude model and Fermi velocity I have answered a question where you are given relaxation time and fermi velocity at 4K and 300K and asks you to work out the mean free path. Easy. Next it says how do these values compare with what...
16. ### Two charge carriers in the Drude model

I'm studying Solid State Physics and I have some problems with a problem. It is stated like this: Consider a system of two charge carriers in the Drude model. The two carriers have the same density n and opposite charge (e and-e), and their masses and relaxation times are m1,m2 and r1,r2...
17. ### Is Free-electron model := Drude Model (of metals) ?

Is the free-electron model synonymous with Drude model? or is Drude model a special subset of the free-electron model? I have seen texts that refer to a "free-electron model" and do not mention Drude's name. and i have also seen texts use these two terms interchangeably. Sorry, i have no...
18. ### Ohm's Law derivation from Drude Model

I'm having trouble understanding the derivation of Ohm's law from the drude model. So you start with a simple sum of forces: \Sigma F_x = - e \: E + F_{collision} = 0 (my understanding is that there are only two forces in Drude's model: those from electron-ion collisions and applied...
19. ### Can the Drude Model Explain Scattering Time in Terms of Unit Conversion?

I got the answer of the hw, but still have question about it. I need to calculate the scattering time μ = eτ / m. τ is the mean time. the unit needs to be in cm^2 / V.S I put the unit like this : e = coulumb τ = s m = kg then it's impossible to get the unit like that. Then I'm...