Mention any two difference between Maxwell Boltzmann, Fermi Dirac and Bose Einstein statistics
Answers
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Explanation:
All 3 statistics describe the distribution of a given number of particles on a given set of states defined by their energy under the constraint that the number of particles (N) , the total energy, and the set of states are fixed and have reached equilibrium, meaning are in the most likely distribution.
The difference between FD (Fermi-Dirac) and BE (Bose-Einstein) is whether the Pauli exclusion principle apply aka whether a state can harbour more than one particle.
Both distributions are approximated by the MB (Maxwell-boltzmann) distribution in the case where the density of particles per state is very small and it no longer matters whether a state can hold more than a single particle. This happens when the total energy is high enough for particles to scatter sparcely unto the set of states aka high temperature.
The probability density distributions are as follow:
P_BE_j = 1/(exp((E_j-u) /(kT) - 1)
P_FD_j = 1/(exp((E_j-u) /(kT) + 1)
P_MB_j = 1/(exp(E_j-u/(kT) )
Where E_j is the energy of state j, k is Boltzmann's constant, and T is the temperature, which is linked one2one with the average energy per particle. The constant u is the normalisation constant and also have profound meaning in physics beyond the scope of this answer (chemical potential, Fermi energy, the partition function if you want to Google) .
For very low temperature aka low total energy per particle, BE have most particles in the state of lowest energy, while the FD has particles in the N lowest energy states.
This is the difference between bosons and Fermi particles as for example light and matter. Light do not collide, matter does.