Bose-Einstein Statistics

Fermi-Dirac Statistics

Maxwell Boltzmann distribution

This statistics is obeyed by identical, indistinguishable particles of integral spin (bosons) that have symmetrical wave functions and is so named as it was devised by Bose for light quanta and generalized by Einstein anddon’t obey the Pauli exclusion principle

These statistics are obeyed by indistinguishable particles of half-integral spin that have anti-symmetric wave function andobey the Pauli exclusion principle.

According toMaxwelldistribution of velocities, avery small fraction of the molecules has either very high or very low velocities.

The major fractionhas avelocityclose to the averagevelocity. It is known asprobablevelocity.

The mathematical form of Bose-Einstein Distribution Law is

\(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}-1}\)

The mathematical form of Fermi Dirac Distribution Law is

\(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}+1}\)

The mathematical form of Maxwell Boltzmann Law is

\(n_i=\frac{g_i}{e^{\alpha+\beta\epsilon_i}}\)