All Problems

Molecules and Crystals

Problem 6.197

Employing Eq. (6.4g),(6.4 g), find at T=0T=0 : (a) the maximum kinetic energy of free electrons in a metal if their concentration is equal to nn; (b) the mean kinetic energy of free electrons if their maximum kinetic energy Tmax⁡T_{\max } is known.

Reveal Answer
 6.197.  (a) Tmax⁡=(3π2n)2/3ℏ2/2m ;  (b) ⟨T⟩=53/Tmax⁡\begin{aligned} &\begin{array}{ll} \text { 6.197. } & \text { (a) } T_{\max }=\left(3 \pi^{2} n\right)^{2 / 3} \hbar^{2} / 2 m \text { ; } \end{array}\\ &\text { (b) }\langle T\rangle={ }^{3 /}_{5} T_{\max } \end{aligned}
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