Does the lorentz force occur at the atomic level?
Does it have a quantized unit?
What do you mean by quantized unit? If you asking about the quantum version of the Lorentz force, it is treated just as any other force in quantum theory.
You can begin with a quantum particle in a classical electromagnetic field.
Say take a Hydrogen atom in a uniform magnetic field. There is the Coulomb force pulling the electron toward the nucleus. If the electron orbits one way round then the Lorentz force will pull it a bit closer to the atom, if it orbits the other way around then the Lorentz force will pull the electron a bit farther from the atom.
The force isn't quantized but the orbital energies of the electron are.
What happens then is that the magnetic field splits the quantized orbital energies. You see this manifest as line splitting in the spectrum aka the Zeeman effect.
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