Why do electrons have band widths or energy bands?

[Alex299792458]

So I know glass is transparent because the electrons have energy bands(or the energy to get it up to the next energy state) that are beyond the energy of visible light. But what I what to know is why do the electrons have energy bands because every single electron is the same and there all fundamental so why do some electrons have small band widths(like the ones in brick) and others have large band widths(like the ones in glass)?

 

[PietKuip]

Brick is aluminum silicates with some iron. The bandwidths are similar to glass, but brick is microcrystalline, glass is amorphous.
The absorption by iron is not due to bands, but to ligand field states and to charge transfer absorption. Red in brick, green in glass.

 

[Alex299792458]

I understand the bands fall in a certain region on the electromagnetic spectrum but why then don't all electrons have the same band width? Is it the nucleus, is it the atoms in the whole molecule, is it the arrangement of electrons in atom? If you look at plane old lead you will see that it is opaque and no light goes through but when you add and oxygen atom to form lead oxide and mix it into molten glass it will form a transparent crystal. But why does this chemical process and all other chemical processes that form a transparent substance change the band width of an electron?

 

[Drakkith]

It's not the electrons themselves that have bandwidth, it is the atoms and molecules of the material. The absorption spectrum of every element, ion, and type of molecule is unique because they all have different numbers of charges in different configurations, which lead to different wavelengths of light being absorbed.

 

[radium]

A band structure of a solid is obtained by solving the schrodinger equation in a system with periodic boundary conditions. You consider overlap between orbitals on the atoms as the possibility for electrons to hop between. In a simplified tight binding model you would basically be considering localized electrons which have a hopping term of some strength allowing them to go between sites. Now when you solve these types of systems, because you are in a periodic system with no open boundary, all the single levels will come together in the limit that the system size goes to infinity (actually all finite systems are gapped unless you have a state at zero energy).

In summary, the band structure will be determined by the both the types of atoms (their orbitals and orbital energies) and crystal symmetry. Glass is amorphous so this does not cover that.

 

[ZapperZ]

So I know glass is transparent because the electrons have energy bands(or the energy to get it up to the next energy state) that are beyond the energy of visible light. But what I what to know is why do the electrons have energy bands because every single electron is the same and there all fundamental so why do some electrons have small band widths(like the ones in brick) and others have large band widths(like the ones in glass)?

Please note that this is why we have a field of study called "solid state physics" or "condensed matter physics". There is a very distinct difference in the properties of matter when it is in a "conglomerate", i.e. when there is a lot of them. An individual atom of carbon behaves very differently than a solid carbon, graphite, and diamond, even though they are all made of carbon. Even arranging the carbon atoms differently can results in a graphite, or diamond, which have extremely different characteristics.

So already this collective behavior of particles will cause very different behavior than isolated particles. The same can be said about electrons, especially electrons in solids. They don't live in an isolated universe. They live in a many-body interaction universe, where they are governed by the lattice potential of the solid, and how close other electrons are. This is why, in a solid, instead of discrete energy levels, one can obtain "bands" instead. This is a characteristics of the interaction of many, many atoms and electrons.

Zz.