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Molecules and Crystals

Problem 6.201

Calculate the interval (in eV units) between neighbouring levels of free electrons in a metal at T=0T=0 near the Fermi level, if the concentration of free electrons is n=2.0⋅1022 cm−3n=2.0 \cdot 10^{22} \mathrm{~cm}^{-3} and the volume of the metal is V=1.0 cm3V=1.0 \mathrm{~cm}^{3}.

Reveal Answer
ΔE=2π2ℏ2/mV(3π2n)1/3=2⋅10−22eV\Delta E=2 \pi^{2} \hbar^{2} / m V\left(3 \pi^{2} n\right)^{1 / 3}=2 \cdot 10^{-22} \quad \mathrm{eV}
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