Questions about Drude model and Sommerfeld model

Physics Q&A
1

Hi,
According to the lecture notes, the first assumption for the Drude model is that ‘‘Electrons scatter randomly at uncorrelated times. The average time between scattering is τ. Therefore, the probability of scattering in a time interval dt is dt/τ.’’ Further on the same page, it mentions that the Sommerfeld model helps justify this assumption. However, I’m still unsure how the Sommerfeld model justifies the idea that electrons scatter from atoms after a constant scattering time τ.

Another query I have pertains to the comparison between the Drude model and the Sommerfeld model in terms of electron velocity. In the Drude model, a very low velocity for electrons was found, with the explanation that despite this slow speed, light immediately flickers upon switching on due to the high propagating speed of the electric field. Conversely, in the Sommerfeld model, a significantly different velocity for electrons is derived, being 0.3% of the speed of light. This raises the question of which velocity we should consider as the true speed of electrons: the slower one from the Drude model, considering the faster propagation of the electric field, or the velocity determined by the Sommerfeld model?

Thanks in advance!

2

the first point is that the Sommerfeld model showed us that only a small fraction of the electron, namely those within k_BT of E_F can contribute to conduction. These electrons approximately have the same velocity, namely the Fermi velocity

To the 2nd point: note that the drift velocity is the net average velocity of the electron gas. The individual electrons can still move extremely rapidly

3

It’s clear now, thank you so much.