Electrons travel at the speed of light. However the speed is slowed down heavily in a conductor and they travel with an average velocity called drift velocity due to the combination of electric field and collisions.
The Fermi level is the surface level at the lowest available energy states where no electrons will have enough energy to rise above the surface. Only those electrons very close to the Fermi energy can participate in ordinary electrical conduction. The conductivity of a material depends on the drift speed and the fermi speed.
Also learn
Matthiessans rule
Wiedmann Franz law
The contents given below are just scribbling notes
From Ohms law
I=V/R
R=rL/A
I=EA/r -------1
Current Density, J=nevdI=nevdA ------------2
From 1 and 2
r=E/(nevd) ------------3
Acceleration experienced by free e-s is =vd/t
Acceleration=eE/me
vd=eE.t/me ---------------4
From 3
r=me/(ne2t) ------------5
Mean free path, l=vav.t --------------6
From 5 and 6
r=mevav/(ne2l)
