*Occupation Probability*According to classical
theory all the electrons in a metal can have the same energy, so that, at 0K,
they all condense into the lowest available energy. But when quantum statistics
is applied we find that these electrons occupy states between the energy values
O and.

Fermi has shown that the probability of occupancy of a particular quantum state is given as

WhereFermi factor or Fermi function. E is
the energy of the given state andis the Fermi energy at temperature T. The
function (1) is plotted in Fig. for various values of T.

Let us consider the
behavior of Fermi factor at different temperature -

**(a) **At T= 0K, the
exponential term whenapproaches to zero asAnd we get.

The meaning offoris that all the quantum states are occupied
and all the states havingare empty at 0K.

**(b)** At,

Hence the probability
of occupation of Fermi level is fifty percent. The plot forandtemperatures is also shown in Fig. The value
ofis still practically unity.

For energies above,
the Fermi distribution becomes identical with that of Boltzman distribution.
The meaning of this is that all the states beloware not filled and hence all the states above **(c)** At very high
temperatures whenthe relation (1.74) does not remain valid and
the entire distribution becomes Maxwell-Boltzmann. This is shown for
temperaturein Fig.

*For next topic 'Effective mass' - Click Here*

## 0 Comments

If you have any doubt, please let me know