Convert Radiant Power Per Nm Into Photon Flux Per Nm

[WeedBulbs]

Spectrum data files from a spectrometer typically have columns for nm (wavelength) and Pe (Radiant Power/Flux in mW), but plants don't give a rip about Radiant Power... they only care about photons of light (Photon Flux). So I have been on a quest to Convert Radiant Power/Flux per nm to Photon Flux per nm. I would have thought this was a common conversion, but after extensive searches did not find any such conversion formulas on the net... so I have been working on making my own. I think I have it correct, but would like someone to check my math. Can someone please help?

 

Specifically, I have made a conversion factor to convert milliWatts(mW) of Radiant Power/Flux per nanometer(nm) of Wavelength... 

into Photon Flux per nanometer(nm) of Wavelength with units of micromoles/second.

So the desired end result formula is ...

PF/nm (μmol/sec) = mW * nm * {conversion factor}

where

mW = milliWatts of power

nm = the nanometer wavelength.

(See conversion factor below.)

 

(note, I am using Excel formula notation)

 

To make the conversion factor, first I start with the formula...

photons/sec = W/(h*c)/λ

where 

W = Watts of power

h = 6.626E-34 J•s (Planck's constant)

c = 299792458 meters per second

λ = wavelength in meters

(h*c)/λ is the energy of one photon

 

Next I convert Watts to milliWatts using

W = mW/1000

so

photons/sec = mW/1000/(h*c)/λ

 

Next I convert photons to μmol using Avogadro's constant...

μmol = 6.022E+17

so

photons/μmol/sec = mW/1000/(h*c)/λ/6.022E+17

 

Next I convert λ in meters to nanometers

λ = nm * 1E-9

so

photons/μmol/sec = mW/1000/(h*c)/(nm * 1E-9)/6.022E+17

photons/μmol/sec = mW * nm * 8.35963112611017E-06

so

{conversion factor} = 8.35963112611017E-06

 

Can someone please check my math for correctness?

(I have attached the spreadsheet to help.)

 

Thanks

Ron

RadiantPowerToPhotonFluxConversion.xlsx