Consider an isolated atom. Its energy levels are discrete. Now consider a metal. In this case, every energy level of the isolated atom is replaced by a band which is composed of very close discrete energy levels. So, because the energy levels of the isolated atom are discrete, in a metal we have bands with allowed discrete energy levels (and these energy levels are very close one to another, as I've said) separated by bands with not allowed energy levels. My question. Are these bands with not allowed energy levels small as the difference between the allowed discrete energy levels within the band with allowed discrete energy levels? So can we consider that the electronic band of a metal is a single broad electronic band? Or the difference is rather large, and in the textbooks they only show us the band where the Fermi level is (without showing us the bands that are below the Fermi level band)? I attached a picture. In the first figure, we see that the difference is rather large. But in the second figure, I see that the electrons occupy everything from energy 0 to the Fermi energy level (so there are no not allowed energy levels like the first figure shows) So, what is happening?