This seems like almost too much of an elementary question, but what properties of metals / insulators cause their bandgaps to differ?
the gap between the two bands of allowed states
For me, it has been a long time that I have reviewed solid state physics, but I believe you are talking about two different things.
The gap between the valence band and the conduction band has (to my knowledge) nothing to do with the wavefunctions of electrons. The energy gap simply explains the energy necessary to extract an electron from the valence band. The electron wavefunction explains behaviour of electrons as a wave-like particle.
Im not sure what hafsa is saying exactly, but in response to ZzapperZs reply the bloch theorem just shows us that a periodic potential causes the separation of energy levels into bands. But a metal is a crystal structure with a periodic potential so why does band theory say that there is not energy gap in a metal?
according to the periodic chart atoms with larger nuclei or with fewer valence electrons tend to be metals. also metals tend to be much denser.This seems like almost too much of an elementary question, but what properties of metals / insulators cause their bandgaps to differ?