# Understanding the collisions of electrons and ion cores in the Drude model

In the free electron gas model, we assume that the conduction electrons are assumed to move freely throughout the conducting material which collide with the ion cores of the lattice.

Image taken from Wikipedia article on Drude Model

Now, I want to know how do these collisions take place. Considering electrons and ion cores as hard balls, the above figure shows that the electrons collide with the ion cores and are repelled by the cores. If this is true,

1. Does a free electron feel any net force when it is not colliding? (Except the force due to applied electric field)

Are the colliding electrons repelled by the outer shells of the electrons bound to the nucleus? I don't think so. The colliding electron should always feel a net attractive force towards the nucleus according to shell theorem because the ion is positively charged. If the colliding electron gets past the electron shells, what does happen now? I imagine two cases:

Case 1

The electron does not hit the nucleus and is deflected due to Coulomb forces.

Case 2

The electron hits the nucleus. Now I don't know what happens afterwards. Does any repulsive force act on electron(strong or weak nuclear forces?)? If yes, does the electron gets reflected as if the electron and the nucleus were hard balls? Or the electron just penetrates the nucleus and emerges from the other side undeflected? Now my question is

1. What is the true mechanism of collisions considered in the Drude model? I think it is case 1 but I'm not sure.
• The picture is wrong (though perpetuated by text books). Electrons aren't hard balls flying around in space, but quantum objects. Actually, electrons move through a perfect lattice without resistance. The collisions are with phonons (that is: thermal lattice vibrations), impurities, defects and with other electrons. – Sebastian Riese Jun 9 '18 at 11:46
• @SebastianRiese I have not learnt quantum mechanics yet so I cannot understand calculations using wavefunctions. I know that Drude model or free electron model is not entirely correct because it is classical; but I want to know if the collisions can be explained in a classical way or not. – Apoorv Potnis Jun 9 '18 at 13:55
• You can build a classical Drude model (after all Drude did develop it as a classical theory), but it will not give you correct results (among other things, because the electrons are a degenerate Fermi liquid). But developing a classical microscopic theory of the scattering of the electrons is probably not very helpful. (If you do the full quantum calculation, then the Drude model will be the result in the right limit, but the correct scattering time $\tau$ is not classically accessible). – Sebastian Riese Jun 9 '18 at 18:22