So the 4.7 umol/j is qer of roughly 3000k. This is the photon count of 3000k spectrum per joule of light output. One of two things will/is occur/ing (A we will hit a ceiling of 3.72 umol) (B the phosphorus is not simply "peeling" energy off each respective photon but rather redistributing the energy)
Can someone please clarify this for me if I'm wrong.
One way to better understand the conversions is to look at the separate activities involved in isolation.
The first is the generating photons of a blue wavelength using the electron gap of the diode. That takes x amount of electrical energy to do and without any further processing produces 3.72umoles worth of radiant energy in that wavelength. Consider the 3.72umoles being a count of photons.
That photon then hits a phosphor coating absorbing it and its energy. This excites the phosphor to generate a photon of a longer wavelength, eg. red. The difference of energy between the two wavelengths mainly results in waste heat which combined from the waste heat from the first activity is dealt with by thermal management. Output using the same x amount of electrical energy produces 4.7umoles worth of radiant energy with a light using more red wavelengths.
Photon to photon, a lower wavelength has more energy than a higher wavelength. It takes less energy to create a photon with a higher wavelength. The end output is that x amount of electricity can produce 3.72umoles of blue photons or 4.7umoles of 3000k photons. Since all we care about is photons, this represents a 26% increase in photon count.
Photosynthesis uses 700nm photons; plants will absorb shorter wavelengths and condition the photon by reducing the energy to increase the wavelength to 700nm. This conversion requires resources for the process and also to manage the waste heat energy. The closer to 700nm each absorbed photon is, the less resources the plant has to use.
The led phosphor conversion process performs a similar function to that of the plant photon conditioning process. Providing as many photons close to the 700nm wavelength is how we can best help the photosynthetic process.
Hope that helps.