Electrical current in metals | energy bands

Why electrical current is possible only with the presence of energy BANDs, rather than discrete energy levels.

Thank you.

 

As far as I understand now, in case of discrete energy levels, electrons can not jump from one atom to another because it would violate Pauli exclusion principle, but in case of energy bands, it is somehow possible. And I am not sure about why is it possible.

 

Suppose we have Beryllium (2s2). As far as I understand electron can jump to the free state without changing its quantum numbers. In case of Beryllium s orbital is fully occupied, thus electron can not jump to s orbital again, and only possibility if it would jump to p orbital, which will require change of L quantum number and change of electron's state. What makes electron to change it's state?

Insulators topic, seems to be more less clear to me.

 

Change of energy would mean change of energy level (principal quantum number), as far as I understand, electrical current is due to jump of electrons within degenerate states, that's why electrical current possible in metals and not in insulators (without changing of energy level).

 

Ok, I am confused now. What is meant by the state then? And what determines when the band is fully packed and when not?

As far as I understand, electrons can be in one of the energy bands which are separated by energy gaps (Kronig Penney model). On each energy band/level can be only certain amount of electrons. In insulators we have elements for which energy bands are fully packed, therefore to conduct a current electron must be excited to the higher energy band, which requires overcoming of energy gap. In case of conductors, energy bands are not packed fully, thus electrons do not have to overcome energy gap to conduct.

Is this correct?