What is the difference between an energy band and an energy level (how, if at all, are they related)?

 

(In summary) my current understanding is that an energy level is "any of the possible discrete energies of an atom, molecule, or nucleus." and that energy bands have something to do with semiconductors.

 

Hopefully very soon my understand will be much greater.

As you said, in atoms you have discrete energy levels, that is the energy of the orbiting electrons falls into discrete values.

 

Now in a solid crystal we have a huge interaction between all these discrete energy levels of the individual atoms. This has the effect of "smearing" out the discrete energy levels into bands. That is electrons can now have continous energy, but between selective values. (unless the electron has enough energy to be free in which case it will be truely continous). There can be band gaps, bands can overlap etc...

 

This is well understood using quantum mechanics, most books on the subject will say something about this, if not consult a book called something like introduction to condensed matter physics.

And it's a band because the electrons can't all have the same energy, due to the Pauli exclusion principle. So the band is, in essence, all of the individual levels, piled on top of each other.

Ok, so in a crystalline substance there are billions of atoms and molecules. Their energy levels, due to the Pauli exclusion principle, cannot all have the same value, as a result they each vary slightly. This creates bands of electron (or moledule?) energy.

 

Is that right?

And it's a band because the electrons can't all have the same energy, due to the Pauli exclusion principle. So the band is, in essence, all of the individual levels, piled on top of each other.

 

Is this the same reason for the reasons behind filling in electrons into orbitals? Such as if you had to model a configuration of titanium you would have to fill the orbitals using the pauli exclusion principal right, and from what you said above, is that the reason you fill the orbitals in such a fashion?

Ok, so in a crystalline substance there are billions of atoms and molecules. Their energy levels, due to the Pauli exclusion principle, cannot all have the same value, as a result they each vary slightly. This creates bands of electron (or moledule?) energy.

 

Is that right?

 

That's the basics of it.

Is this the same reason for the reasons behind filling in electrons into orbitals? Such as if you had to model a configuration of titanium you would have to fill the orbitals using the pauli exclusion principal right, and from what you said above, is that the reason you fill the orbitals in such a fashion?

 

Yes, though there are other rules that come into play that tell you the order to fill them. The Pauli exclusion principle tells you why there are two electrons (two different spin orientations) in each sublevel, and no more.