Richard Clark wrote:
The wavelength of the emitted photon is the path length the
electron follows spiraling from one orbital to the other (DeBroglie
wave).

Actually, I think it's more of a quantum thing - a function of the band
gap energy E, which is equal to hv (read h nu) where h is Planck's
constant. Wavelenth is of course related to v by a constant, c (speed
of light). Lambda = c/v. So wavelength = hc/E. If it was a DeBroglie
thing, wavelength would depend on the momentum of the particle as h/p.
The band gap energy is not determined by the energy carried by the
particle, (or by the length of its path), but by the atomic nature of
the material comprising the LED, and the difference in energy between
the conduction band and the valence band of that material.

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