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In a hydrogen atom, the electron can take only certain energies (quantized energies) only. When two hydrogen atoms come close, the electrons can take up more energy states but still the states are quantized.
We can notice that this applies to all electrons in the universe. No matter how far from the hydrogen cluster the electron is found, if we then measure its energy, it shows quantized energies only.
We can repeat this process with semiconductor clusters too. In a cluster with large number of atoms, the energy states will be like bands. Many bands with gaps separating them or may overlap. So all electrons in the universe will have energies that is present in the spretum.
Now when we study junctions between two types of semiconductors, they represent it by a graph. On the$x$ axis they vary position in space. And on the$y$ axis they represent the energy states (bands) available. There are certain energy states before crossing the junction point in x axis but after crossing the junction, the energy states shift. My question: how can it be possible that the available energy states depend on position in space? My argument in the beginning suggests that available energy states don't depend on location.Here's what I mean by the band structure.
1 Answer1
No matter how far from the hydrogen cluster the electron is found, if we then measure its energy,it shows quantized energies only.
This is not correct! An electron of a hydrogen atom can have arbitrary ("unquantized") energies beyond the ionization energy. The same holds for electrons of solids, or any molecule or assembly of atoms where electrons are bound.
My question is that how can this even be possible that the available energy states depend on position in space?
Bound states in different atoms can have different quantized energy levels at different locations. Similarly, the quantized energy spectra (including band gaps) of different solids like semiconductors at different locations can be different and are thus dependent upon position in space. This is frequently used in heterojunction semiconductor devices.
- $\begingroup$"Bound states in.....",this would mean that measuring the energy of an electron we can guess which atom it belongs to.But in a collection of atoms,the electron dosent belong to a particular atom.The orbitals are created as a whole for all electrons by the contribution of all the atoms.$\endgroup$S K– S K2025-11-09 19:11:35 +00:00CommentedNov 9 at 19:11
- $\begingroup$@SK - You are right, electrons with energies in the theoretical energy bands of an infinite solid are delocalized. But considering a finite piece of solid or collection of atoms you still can still know that it is (or was) localized there!$\endgroup$freecharly– freecharly2025-11-09 19:20:03 +00:00CommentedNov 9 at 19:20
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