08-16-2017, 10:58 PM
[attachment=7941]
CONDUCTIVITY ,FERMI LEVEL ,
MEAN FREE PATH &
RELAXATION TIME
FOR TYPICAL MONO-VALENT METALS
IS SHOWN IN TABLE
The conductivity may be obtained experimentally .
Further we can get by using eqn given below
= ( n*Qe2 * )/me --(1)
but obtained may not be accurate but we will get an idea of magnitude of . In a monovalent metal no of free e- /m3 is equals the no of atoms /m3 . From table we find that relaxation time T is of the order of 10-14 sec .Thus we can say that T is extremely small for monovalent metals.
from eqn. given below we can calculate mean free path -
= Vx * c --(2)
The relaxation time for metals refers to e- with Fermi velocity Vf .For usual values of temp. T , it may be shown that the scattering in these monovalent metals is isotropic . Then<cos >, =tc & = Vx * c .The values of man free path at 0 0c are several hundred angstroms.
We find from the graph shown that as we goes on reducing the temp of a metal then it s resistivity also decreases & vice versa but assume a constant value of temp. below 6 K.
In general, the resistivity of a perfect, pure single crystal of a metal approaches to zero as temp. T approaches zero. This signifies that at very low temp. the mean free path assumes microscopic values .This concludes that the earlier discussions are not individual ion cores.