Conduction and valence band for metals

[thinktank1985]

for metals the conduction and valence bands overlap. So how do you distinguish between the conduction and valence bands? How do you find out the lower limit of the conduction band and the higher limit of the valence band?

Or is it the case that the highest conduction band in a metal goes from a value of E=-k eV to infinity eV?

 

[cortiver]

It sounds as though you're thinking of a band only as a range of energy values, which is not accurate. Each band basically consists an electron wavefunction for each value of the wave vector k. If the valence band and conduction band overlap, then there is a valence band wavefunction and a conduction band wavefunction with the same energy, but they're still going to be different wavefunctions. Also, you can get from any wavefunction in the valence band to another continuously by varying k, but you can never get to the conduction band this way.

(As an analogy, you could think about sound waves and electromagnetic waves. They could both exist at the same frequency, but we think of them as distinct because: 1. they are clearly oscillating in a different way, and 2. there's no way you can transform one continuously into the other)