All Problems

Molecules and Crystals

Problem 6.197

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