Why do electrons have band widths or energy bands?

In summary, the behavior of electrons in solids is different from isolated particles due to their many-body interactions, resulting in bands of energy levels instead of discrete levels. This is influenced by the lattice potential and proximity to other electrons. This explains the different bandwidths of electrons in different materials, as seen in the example of glass and brick.
  • #1
Alex299792458
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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)?
 
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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
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  • #5
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.
 
  • #6
Alex299792458 said:
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.
 

Related to Why do electrons have band widths or energy bands?

1. Why do electrons have band widths or energy bands?

Electrons have band widths or energy bands because of the way they behave in a solid material. In solids, electrons are restricted to specific energy levels, resulting in the formation of bands or ranges of allowed energy levels.

2. How do energy bands affect the properties of materials?

The energy bands of a material determine its electrical and thermal conductivity, as well as its optical and magnetic properties. The width and position of these bands also affect the material's strength, hardness, and other mechanical properties.

3. What determines the width of energy bands?

The width of energy bands is determined by the arrangement of atoms in a solid material. The spacing between atoms and the number of electrons in the material's outermost energy level are the key factors that determine the width of energy bands.

4. Why do some materials have wider energy bands than others?

The width of energy bands varies among different materials due to differences in their atomic structures and bonding. For example, materials with strong covalent bonds tend to have narrower energy bands, while materials with weaker metallic bonds have wider energy bands.

5. How do energy bands explain the electrical conductivity of materials?

The energy bands of a material determine its electrical conductivity by allowing or restricting the movement of electrons. Materials with partially filled energy bands and a small band gap between the valence and conduction bands are good conductors, while those with fully filled bands or a large band gap are insulators.

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