6a.1 At sufficiently high temperatures wherein eB(E-μ) > 1, (and sufficiently low number of particles to satisfy the classical limit), show that the Fermi-Dirac and the Bose-Einstein distributions can be approximated by the Maxwell-Boltzmann distribution. eß(E-μ) » 1 → e(E-μ)/KBT 1 f(ε) = eß(ε-μ) +1 >> 1 (ε-μ) » KBT 1 eß (ε-μ)

Physics for Scientists and Engineers with Modern Physics
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Chapter41: Atomic Physics
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6a.1 At sufficiently high temperatures wherein eß(E-μ) >> 1, (and sufficiently low number of particles to
satisfy the classical limit), show that the Fermi-Dirac and the Bose-Einstein distributions can be
approximated by the Maxwell-Boltzmann distribution.
eß(ε-μ) » 1 → e(E-μ)/kgT » 1
1
f(ε) =
eß(E-μ) + 1
→ (ε -µ) » kBT
1
eß (ε-μ)
Transcribed Image Text:6a.1 At sufficiently high temperatures wherein eß(E-μ) >> 1, (and sufficiently low number of particles to satisfy the classical limit), show that the Fermi-Dirac and the Bose-Einstein distributions can be approximated by the Maxwell-Boltzmann distribution. eß(ε-μ) » 1 → e(E-μ)/kgT » 1 1 f(ε) = eß(E-μ) + 1 → (ε -µ) » kBT 1 eß (ε-μ)
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