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?
Ron
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?
Ron