How is light created at the atomic level?
Atoms are composed of nuclei, agglomerates of protons and neutrons, which have electrons in orbitals around them; as many electrons as protons so that normally atoms are neutral.
What keeps atoms stable is that the orbitals exist at specific energy levels given by the solution of the potential problem in quantum mechanics , of a charge in the potential well of another charge, for example the hydrogen atom. At the micro level, the charges do not orbit around their center of mass system but are described as probability distributions that tell us the probability to be found in a specific (x,y,z) space point.
The carrier of the electromagnetic interaction is the photon, an elementary particle which obeys the quantum mechanical form of the Maxwell equations. It has spin 1 and zero mass and it carries the electromagnetic energy as h*nu where h is the Planck constant and nu the frequency of the wave that can be built up from an ensemble of such photons.
The electrons of the atoms are usually at the lowest orbital. Above the filled energy levels there exist orbitals that the potential predicts but are unfilled. A disturbance of the electron in its orbital, by thermal interactions of atoms for example, can kick an electron to such a higher orbital When it falls back in the ground state it was before the disturbance, electromagnetic energy is radiated, in the form of a single frequency photon that has the energy of the difference between these two orbital energy levels.
This is the black body radiation that mass of atoms at a certain temperature emit, called black body radiation when in an ensemble, as from the radiation of the sun.
An ensemble of photons, zillions of them, build up the classical electromagnetic wave which statement can be shown mathematically, but is not a simple formula. If you are interested read up this blog entry by Motl.
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