kT = v2th 
F = eE ........(1) 
Force F = ma …....(2) 
ma = eE or a = …......(3) Acceleration (a) = Or a = 
So vd = a ……….(4) 
vd = = E ……….(5) vd = E ……….(5a) 
J =E ……….(6) Or = 
J = nevd ....... (7) 
J = neE Or = 
= ....... (8) = ....... (8a) 
Resistivity ρ ρ = = 
= So = = Also ρ = = 
μ= ....... (9) 
J = nevd 
J = neμE Or = μne ....... (10) 
= μne μ = 
λ = ………(1) 
. T ……….(2) 
λ = ………..(3) 
ρ = ..…………..(4) 
ρ T ..……….(5) 
………….(6) 
vg (1) 
E ℏ and p ℏk (2) 
vg (3) 
= = (4) 
F = m (5) 
F = (6) 
(7) 
In metals, the Fermi energy gives us information about the velocities of the electrons which participate in ordinary electrical conduction. The amount of energy which can be given to an electron in such conduction processes is on the order of microelectron volts (see copper wire example), so only those electrons very close to the Fermi energy can participate. The Fermi velocity of these conduction electrons can be calculated from the Fermi energy.
This speed is a part of the microscopic Ohm's Law for electrical conduction. For a metal, the density of conduction electrons can be implied from the Fermi energy.  Figure 12: Fermi level for a Semiconductor

n(E) = (1) 
F(E) = = = 1 
F(E) = = = = 0 
F(E) = = = = 50% 