Question

In the band diagram of potassium, the valence band would be:

a) completely filled

b) partially filled

c) completely empty

d) nonexistent

I know the answer is a), but could someone clearly explain to me why this is?

Answer 1

According to the definition of the valence band and conduction band, the valence band is defined as the band is the highest band which is completely filled at absolute zero and the next band which is either partially filled or completely empty is called conduction band.

So at absolute zero temperature, the valence band is always completely filled independent of the material and indeed by the definition of valence band the option ''a.'' is correct.

Further at zero temperature as I said the valence band is completely filled and conduction band may be partially filled or completely empty as they are separated by a band gap. But at a non-zero temperature, you cannot say that valence band of a material is completely filled because at a non zero temperature the conduction band (band next to the valence band ) have always a non-zero probability(due to Fermi function) that its states are filled with electron so it is always partially filled at non-zero temperature.

In conclusion, it can be said that the valence band is always completely filled at absolute zero but at non zero temperature it is always partially filled.