Explaining the Continuous Diffraction Spectrum of a Heated Solid

[rtareen]

TL;DR

Book is Sears and Zemanskys University Physics 14E. Book explains that the discrete line spectra of a heated gas are due to electrons occupying specific energy levels and thus they only emit certain frequencies according to E = hf. But then what about the continuous spectrum of a heated solid as seen in the figure?

This is the figure from the book. First of all, from what I know about diffraction, there is an interference pattern but not dispersion of the different colors. If what is happening here can be explained that would be great.

Second, the book says the line spectra for different gasses are due to only certain energy levels being occupied in the atom, and the frequency is determined when an electron drops an energy level by E = hf. But then what about the heated filament which is also made up of atoms?

Also, how many energy levels can an atom have? If it differs per element, is there a way of finding out easily?

EDIT: Second question was answered two sections later. But my first and third questions remain.

 

[Charles Link]

With a diffraction grating you do get a dispersion that is similar to what a prism gives, but you will get multiple rainbows that may overlap somewhat, due to the various orders of the maxima.
The primary interference maxima occur at $\theta$ such that $m \lambda=d \sin{\theta}$. The secondary maxima are very numerous, but insignificant for a grating with many lines.
The primary maxima formula tells you how the dispersion occurs as a function of wavelength.

 

[f95toli]

Solids are quite different from gases simply because the atoms/ions in a solid are -by definition- connected to each other. One consequence of this is that you no longer have discrete energy levels in the same way as you have in free atoms; there are plenty of electrons that are able to move around in the material and are no longer tightly bound to specific ions so they are no longer limited to having specific energies.
Hence, the reason why you see a continuous spectra is simply that the underlying energy distribution in a solid is continuous.