Microscopic View of Ohm's Law (courtesy of GSU)
The current density (electric current per unit area, J=I/A) can be expressed in terms of the free electron density as:

The number of atoms per unit volume (and the number free electrons for atoms like copper that have one free electron per atom) is:

From the standard form of Ohm's law and resistance in terms of resistivity:

The next step is to relate the drift velocity to the electron speed, which can be approximated by the Fermi speed:
Fermi Speed
 $$v_F = \sqrt{2E_F \over m}$$ where: vF = Fermi speed EF = electric field m = mass
The drift speed can be expressed in terms of the accelerating electric field E, the electron mass, and the characteristic time between collisions.
Drift Velocity of Electron
vd =
 eEm τ = eEm dvF
where:
vd = drift velocity
e = charge of electron
E = electric field
m = mass of electron
τ = electromagnetic decay
d = distance between atoms
vF = Fermi speed
The conductivity of the material can be expressed in terms of the Fermi speed and the mean free path of an electron in the metal.
Conductivity
σ =
 ne2dmvF
where:
σ = conductivity
n = free electron density
e = charge of electron
d = distance between atoms
m = mass of electron
vF = Fermi speed