## question about level splitting in band theory

Hello ,

about the band theory I was confused some how

seeing the attached image I ask :-

1- when the atoms are far away we take a single atom alone as a system , but when atoms get closer we identify them all as the system , right ?!

2- why do we use the word " splitting" , why don't we say that every atom contributes with its _ for example_ 2s level and so the overall 2s can carry more electrons ?!

3- does the whole band have the same energy ?! if so why do we represent the increase of electron's energy by farther " rising" in conduction band ?! and if not why is there difference in energy ?!

4- I have to say that i'm studying this as an introduction to semi-conductor devices not physics course .
Attached Thumbnails

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 1. yes. 2. Its just a choice of word. When describing the graph it seems as if the line is split into two. 3. No. The difference in energy is due to orbital overlap integral. 4. Hahaha. If you wanna dig deeper into semiconductor you better learn the physics anyway.
 To give an informative but non-exact picture, you can first imagine a charge q that has a lot of discrete energy levels around. If you increase the amount of the charge, these levels would get closer to each other (and when you make two atoms close together, it is like that you have a bigger system with larger amount of charges and closer energy levels) so that in the limit you gather a lot of atoms, the levels get very close and make a continuous energy band.

## question about level splitting in band theory

1 far away enough that they do not affect each other, that is why we regard them as two alone systems.
2 "splitting" is referring to the energy,
3 of course different as the picture implies due to Pauli's exclusion principle,