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Difference between maxwell boltzmann distribution and fermi dirac distribution

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apply to “CLASSICAL” particles with non-quantized energy levels.

Bose–Einstein statistics apply to quantum particles with the property that any NUMBER of particles can occupy any level. It turns out these are the particles with integral “spin” such as photons and He4 (but not He 3) atoms.

Fermi–Dirac statistics - apply to quantum particles with the property that only ONE particle can occupy any particular level. It turns out these are the particles with half-integral “spin” such as electrons and neutrons.

Both BE and FD statistics converge (from opposite directions) on MB statistics when the density of particles is small COMPARED to the Quantum concentration, where the inter-particle distance is COMPARABLE to the de Broglie wavelength


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