I am not a physicist or mathematician, but this formula is not correct - there is nothing in there to account for the number of LEDs. You get the same number with this formula for 1 LED as you do 10,000 LEDs.
It looks impressive to throw out physics terms like Planck's constant, but is not a valid formula.
I made mistake by writing it into forum, I have the formula in Excel table. I did correct the formula in my next post:
PAR/W = lambda / (c . h . NA) in mol of photons.m-2.s-1
h = 6.6626E-34 (Planck's constatnt)
c = 299792458 (Speed of Light)
NA = 6.02214E23 (Avogadro's number)
lamdba = 450nm = 4.5E-7 m (wavelength of Royal Blue)
Look at http://en.wikipedia.org/wiki/Photon
you can see there that energy of Photon is E = c. h / labmda in J (W.s-1)
Then look at Example problem #2 and #3: where they calculate inverse KJ/mol as E multiplied by Avogadro number. 241 KJ/mol inverted is 4.14E-6 mol/J (same result as you get from 496.36nm / (299792458 . 6.6626E-34 . 6.02212E23 ) = 4.13E-6 mol / J = 4.13 umol/J
http://www.chemteam.info/Electrons/LightEquations2.html
If we invert the equation we get umol/J and J per one second is Watt. So in the final we get umol/W formula:
umol/W = 1/ (E . Na)= lambda / (c . h . NA)i
The result you get is how many PAR you get from 1W of Radiant flux of Royal Blue per square meter. Cree XP-E Royal Blue gives you 500mW at 350ma, at 700ma around 900mW. If you get 3.76 umol for 450nm light then from 0.9W RB radiant flux of 2.4W (700mA*3.4V) of RB led you should get 3.4 umol.
If you put 41 Leds (~100W consumption) in one square meter you get average 41x3.4 = 140 umol per square meter. Focused in smaller area e.g. into 50x25 tank (0.75 sq. m) you get 140 / 0.75 = 187 umol/s into water surface of your tank.
To me it perfectly correlates with other calculations such as umol/lux, etc.
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