All Problems Molecules and Crystals
Problem 6.202
Making use of Eq. \((6.4 \mathrm{~g}),\) find at \(T=0\) : (a) the velocity distribution of free electrons; (b) the ratio of the mean velocity of free electrons to their maximum velocity.
(a) \(d n_{v}=\left(m^{3} / \pi^{2} \hbar^{3}\right) v^{2} d v\) (b) \(\langle v\rangle / v_{\max }=3 / 4\)