Looking at the periodic table: group II elements like magnesium, potassium are known to be metallic, and yet, they have a full outer shell. So, this means that they should have completely full (valence) bands.

Now, last time I checked a completely full band does not conduct.

In a similar way, group IV elements like silicon and germanium, and tin (which is practically a metal!) are actually semiconductors. But, diamond is an insulator.

I am an undergraduate of physics (and a newcomer to this site), I would love to understand the resolution to this problem. I have just started learning solid state physics so my knowledge is somewhat limited.

But, why do group II elements conduct and group IV elements not act like semiconductors?

Thanks.