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What is Allowed orbit applied to?

Updated: 4/28/2022
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In quantum mechanics, when applied to an isolated atom, an allowed orbit can refer to the spacial path of an electron which satisfies the Schroedinger Equation. This allowed path can be interpreted as the balance between kinetic energy (electron motion) and potential energy (proximity to nucleus) which returns a single energy. In band theory of solids, allowed states are defined by the bragg diffraction condition, which is constructive or destructive interference based on wavelength. Since electrons can be regarded as a particle or wave, an electron with a certain momentum has a wavelength (classically defined as: p = mass x velocity, but de broglie relation: p = constant / wavelength). Since there is a set distance between atoms in a material, this spacing determines which wavelengths destructively interfere, or cannot propagate, throughout the material. This means that electrons at a certain kinetic energy (related to motion) cannot exist, given the position of atoms. It should be noted that the "allowed states" in multi-atomic systems are a continuous range (or "BAND") of kinetic energies that an electron can adopt in a material. As there are FEWER atoms that comprise the material, the BAND thickness of allowed states grows NARROWER. In the case of a SINGLE atom, the continuous range collapses to a single line, corresponding to ONE energy of an allowed orbital. References: http://en.wikipedia.org/wiki/Band_theory

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Q: What is Allowed orbit applied to?
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