# BAND THEORY : Overlapping energy bands in metals

I have been studying Energy bands and suddenly I encountered a diagram in which the two bands(valence and conduction) overlaps in case of metals. What is the meaning of this overlapping? Suppose they overlap from $\mathrm{-2\ eV \ to \ 4 \ eV}$, it means that electrons belonging to these energy levels belongs to both valence as well as conduction band? Isn't it senseless? How an electron in the valence shell can be a valence shell electron too and a conducting/free electron too?

Any help would be higly appreciated from any brother/sister.

• There is more to the electronic structure than just energy. The electron wave functions have different wave numbers (reciprocal of wavelength) on which the energy depends. These dispersion relations are different in different directions in the crystal. But the decisive thing for conductivity is whether there is an energy gap or whether there is overlap of partially filled bands. – Pieter Jan 11 '18 at 20:54
• I'm in Grade $12$. I don't know higher quantum mechanical physics! Please explain it as per the level of Class $12$ Students. – Selena Jan 11 '18 at 20:56
• It is very difficult to explain. The concept of reciprocal space ($k$-space, k is the wave vector) is very abstract. It is a Fourier transform of the crystal, so $k$-space is also a thing in three dimensions. And it is not necessary to understand diodes etc. – Pieter Jan 11 '18 at 21:05
• But what about my this question Sir? This is from my class 12 Book, how can i explain it? – Selena Jan 11 '18 at 21:08
• Rather than thinking of them as overlapping, just think of it as one band which is not full. Therefore electrons can "move around". – Steeven Jan 11 '18 at 21:27

• $\mathrm{4th}$ para was actually helpful! Thanku! – Selena Jan 12 '18 at 10:16