1000 Solved Problems in Modern Physics

292 5 Solid State Physics

The total energy of the lattice is the sum of the attractive and repulsive energies

U=−NA

e^2

r

+

b

rn

(5.3)

whereNis the number of molecules andAis known as the Madelung constant.
For equilibrium
dU
dr

= 0 (5.4)

The force is

−

dU

dr

= 0 (5.5)

The current density

J=i/A (5.6)

whereAis the cross-section of the conductor.
The drift speed
vd=j/ne (5.7)

wherenis the number of conduction electrons per unit volume. The resistivity is
given by

R=ρL/A (5.8)

The conductivity is given by

σ= 1 /ρ (5.9)

vd=eEτ/m (5.10)

whereEis the electric field andτis the mean time between collisions.

ρ=me/ne^2 τ (5.11)

τ=meσ/ne^2 (5.12)

The mean free path
λ=τ (5.13)

Hall effect

If a thin strip of material carrying a constant current is placed in a magnetic field
Bperpendicular to the strip a potential difference appears across the strip. This is
known as Hall effect.

E=jB/qn (5.14)