Discussion
The distribution function for identical indistinguishable particles can be represented by the equation \(N_{j} = \dfrac{g_{j}}{e^{(\epsilon_{j}-\mu)/kT} + a}\), which of the following statements is correct ?
Answer: C
The correct statement is a = +1 for Fermi-Dirac statistics.
The general distribution for indistinguishable particles is
\[ N_{j} = \frac{g_{j}}{e^{(\epsilon_{j}-\mu)/kT} + a} \]
For fermions, which obey the Pauli principle, a = +1, so Nj/gj can never exceed 1. For bosons a = −1, which lets many particles crowd into one state. With a = 0 the expression reduces to the classical Maxwell-Boltzmann distribution.
So options A and B have the signs swapped between the two statistics, and a = 1/2 (option D) corresponds to no standard statistics.
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