# Debye Temperature for Copper

There are few things going on here. The first is that you seem to be mixing units for density and the molar mass, using kg in one case, and g in the other. If you fix that, you will correctly get a number density on the order of $10^{28}$. However, you still won't find good agreement with the $~345K$ value you expect. Why is this?

Well, there's a second and subtler thing going on, which is that you are using a single speed of sound. In reality, the speed of sound is different in the (one) longitudinal and (two) transverse directions. If you instead use a mean speed calculated through $$\bar{v}_s = 3^\frac{1}{3}\left( \frac{1}{v^3_{\mathrm{transverse}}}+\frac{2}{v^3_{\mathrm{longitudinal}}}\right)^{-\frac{1}{3}} $$ you'll get a lot closer to the experimental value. You'll note that this isn't an ordinary average velocity, it's simply a constant defined in the derivation of the Debye temperature.

The third thing worth mentioning is that the speed of sound is going to depend on how your sample of copper was made. The value $v_s=3800$m/s is the longitudinal sound speed in thin copper rods, whereas $v_s=4600$m/s is a (rather low) value for the bulk material.