Einstein's theory for specific heat

[Titan97]

I have uploaded a page from my prof's lecture on specific heat.

Its given that average energy for each vibrational mode is $$\frac{h\nu}{e^{\frac{h\nu}{T}}-1}$$

Hence $$U=(\text{number of vibrational modes)}\times\frac{h\nu}{e^{\frac{h\nu}{T}}-1}$$

In the lecture slide, the number of vibrational mode is 3N. Is this for a monoatomic structure? Because it doesn't consider rotational degree of freedom.

 

[nasu]

There is no rotational mode in Einstein's model.
He models the crystal as a collection of uncoupled harmonic oscillators, all oscillating with the same frequency.

And if we switch to more realistic models like Debye's or to experimental results, the specific heat of solids around room temperature is due to lattice vibrations only.