Drude Model: Electrons & Collisions

In summary, the Drude model assumes that electrons move in a random direction after each collision, resulting in a mean velocity of -eEτ/m. This assumption has been questioned, as it doesn't seem likely that the direction of the velocity after collision will be completely random. However, the equation for the displacement of a Fermi sphere includes a δk term, which may represent the variation of k. More clarification is needed on the interpretation of this equation.
  • #1
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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 (*), if the electron has a velocity in the direction of the field and suffers collision with another electron, it does not seem likely that the direction of the velocity of the 2 electrons after collision will be completely random.
 
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  • #3
That was quite helpful. Now I don't suppose you could help me interpreting another
l) states that the equation for the displacement of a Fermi sphere is (all h's are hbars):
h(d/dt + 1/τ)δk = F
Now Newtons law for a completely free electron is:
hdk/dt = F
Why have they put in a δk, and how is the equation to be interpreted? Does it represent the motion of the Fermi sphere in steady state?
 
  • #4
Probably the variation of k ...

You would get more attention by posting a new question.
 

1. What is the Drude Model?

The Drude Model is a simplified classical model used to explain the behavior of electrons in a metal. It assumes that the electrons are free to move throughout the metal and are subject to collisions with other electrons and the metal ions.

2. How does the Drude Model explain the conductivity of metals?

The Drude Model explains conductivity by suggesting that electrons move freely through the metal when an electric field is applied. However, collisions with other electrons and metal ions cause the electrons to scatter, which results in a net drift of electrons in the opposite direction of the electric field, creating a current.

3. What are the key assumptions of the Drude Model?

The Drude Model assumes that the electrons in a metal are free to move and that they experience collisions with other electrons and metal ions. It also assumes that the electrons have a random thermal motion and that their average velocity is zero. Additionally, the model assumes that the electric field is the only force acting on the electrons.

4. How does the Drude Model explain the temperature dependence of resistivity?

The Drude Model suggests that at higher temperatures, there are more collisions between electrons and metal ions, resulting in a higher resistivity. This is because the thermal motion of the electrons increases at higher temperatures, causing more collisions and hindering the flow of electrons.

5. What are the limitations of the Drude Model?

The Drude Model is a simplified model and does not take into account the quantum nature of electrons. It also does not consider the effect of the crystal structure of a metal on its electrical properties. Additionally, the model fails to explain phenomena such as superconductivity and the Hall effect.

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