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Molecules and Crystals

Problem 6.206

Find the refractive index of metallic sodium for electrons with kinetic energy \(T=135 \mathrm{eV}\). Only one free electron is assumed to correspond to each sodium atom.

Reveal Answer
 6.206. n=1+U0/T=1.02, where U0=Tmax⁡+A,Tmax⁡==(3π2n)2/3ℏ2/2m.A is the work function. \begin{aligned} &\text { 6.206. } n=\sqrt{1+U_{0} / T}=1.02, \text { where } U_{0}=T_{\max }+A, \quad T_{\max }=\\ &=\left(3 \pi^{2} n\right)^{2 / 3} \hbar^{2} / 2 m . A \text { is the work function. } \end{aligned}
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