Kittel's Solid-State Physics: Finding Cutoff Frequency \omega_D

[ehrenfest]

Homework Statement

This question refers to Kittel's solid-state physics book.

Above equation (23), Kittel says that a cutoff frequency $\omega_D$ is determined by (19) as" and then he gives equation (23). I have absolutely no idea where equation (23) comes from.

Homework Equations

The Attempt at a Solution

 

[genneth]

Could you reproduce the equations for those of us who don't have the book handy?