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Molecules and Crystals

Problem 6.202

Making use of Eq. (6.4 g),(6.4 \mathrm{~g}), find at T=0T=0 : (a) the velocity distribution of free electrons; (b) the ratio of the mean velocity of free electrons to their maximum velocity.

Reveal Answer
(a) dnv=(m3/π2ℏ3)v2dvd n_{v}=\left(m^{3} / \pi^{2} \hbar^{3}\right) v^{2} d v (b) ⟨v⟩/vmax⁡=3/4\langle v\rangle / v_{\max }=3 / 4
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