# Want an equation that calculates power/m2 from concentration of photons and wavelengt

1. Nov 18, 2012

### corvuscrypto

Hello all of you very bright physicists,

The local physics dept. is not answering us thus far and long story short we need a rough estimate of the power of a light source based on wavelength and a measured concentration of photons.

We need a method of converting the photon concentration per area per second (umol*m^-2*s-1) into power, ideally watts per area. We know the wavelength (or range of wavelengths) and the end goal is again to be able to estimate the power we are getting from a light source at a particular wavelength.

The measurements we took were with a photometer that read the concentration of photons for all wavelengths between 300-700 nm. However, we decided that for easier estimation we would use the middle of the range (500nm) and use that as the wavelength to calculate power.

If I counted right, I'm asking for an equation that is a function of concentration and wavelength :P.

Hope that is enough information for y'all to help me out. Even a base set of equations would be nice so I could at least attempt to derive something from them. Any help is greatly appreciated.

Love,

a lowly biologist

2. Nov 18, 2012

### haruspex

Re: Want an equation that calculates power/m2 from concentration of photons and wavel

The energy of one photon is hc/λ, where h is Planck's constant, c the speed of light and λ the wavelength.
Whether using the middle value of the range for the wavelength gives an accurate enough answer will depend on the power spectrum.

3. Nov 18, 2012

### corvuscrypto

Re: Want an equation that calculates power/m2 from concentration of photons and wavel

ok nice, so can I assume that the work being exacted by photon is equal to its energy?

so that would mean W=nhc/λ, and power would be (n*h*c)/(λ*t)...

would it follow that watts/m^2 for my needs is simply [(NsubA*x*h*c)/(λ)] where x is my measured units as stated previously? *NA being avogadro's constant of course

edit: don't worry about the details of power spectra. I will be doing the necessary filter experiments to determine that later, I just needed the equation :D.

4. Nov 18, 2012

### haruspex

Re: Want an equation that calculates power/m2 from concentration of photons and wavel

Whoa, what's Avogadro's constant to do with it? (I did notice "umol" in the OP, but assumed it meant something else in this context.) Is it that there's a known relationship between the photon density and the density of some molecule?

5. Nov 18, 2012

### corvuscrypto

Re: Want an equation that calculates power/m2 from concentration of photons and wavel

well avogadros constant is just to account for the fact that the equation you gave me is for only one photon. I simply scaled it using avogadro's number so I could directly input my measured value. I didn't modify it further to account for the micro factor, but I would in the end result.

6. Nov 18, 2012

### haruspex

Re: Want an equation that calculates power/m2 from concentration of photons and wavel

In the OP you imply you know the photons per unit area per second (though you don't explain how). Why don't you just use that? Avogadro's number is for determining the number of molecules in a volume of gas.

7. Nov 18, 2012

### corvuscrypto

Re: Want an equation that calculates power/m2 from concentration of photons and wavel

Avogadro's is used to define a mol of anything really and even the instrument assures that the number of micromoles of photons is indeed a measure of n*6.022x10^17 photons. That aside, I can't use that measurement only as it measures the flux. I needed power. The instrument measures in micromoles per area per time. Sorry if I was unclear.

Does that change the base energy equation at all?

8. Nov 19, 2012

### haruspex

Re: Want an equation that calculates power/m2 from concentration of photons and wavel

Fascinating. I'd no idea light densities were measured in such units. I only knew about foot candles and Lux. So, it's a bit artificial, but I guess it has some benefits.
So long as you have the conversion factor between those units and actual numbers of photons then that should be fine.

9. Nov 19, 2012

### Staff: Mentor

Re: Want an equation that calculates power/m2 from concentration of photons and wavel

You need to know the photon flux as a function of wavelength. Since you are biologist, I assume you are interested in the solar photon flux hitting the ground. The photon flux at the top of the atmosphere has been tabulated by atmospheric scientists over specific wavelength intervals (much smaller than the entire visible spectrum). Get a book on atmospheric science which has the table or look it up with Google. To get the photon flux at the ground, you need to take into account absorption and scattering in the atmosphere by atmospheric gases and clouds. Very little solar radiation reaches the ground in the UV B.

10. Nov 19, 2012

### corvuscrypto

Re: Want an equation that calculates power/m2 from concentration of photons and wavel

Well technically I'm what's called a biochemist. Our experiment has nothing to do with solar flux or anything environmental. We are testing a new set of drugs that become activated by direct irradiation by light after cell uptake in drug-resistant bacteria and we are optimizing the parameters of the light emission. It is theorized that peak activity is around 400-500 nm, and unfortunately with these compounds we can't just use UV-VIS spec to determine peak absorbance for activation as it changes once it binds to the cell components. We tried fluorescence microscopy but due to focal points in the cells we were unable to determine the peak absorbance wavelength from that. Essentially you have to think of these things as little spherical lenses which changes the game. There is a lot of theory that unfortunately can't be applied because when you factor in biological activity there is too much going on to stick to the simple methods.

So what this equation that haruspex helped me out with (TY btw :D) allows us to measure is the amount of energy that we are irradiating a drug-treated culture of bacteria with. We then look at the inhibition of the bacteria and see what wavelength is most effective. This is where determining the power spectra is important. It is so we can keep the amount of energy being driven into the cells constant, allowing us to determine the most effective wavelength(s) to use. We could do the same thing with a spectroradiometer, but pftttt they are wayyyy out of our budget range.

The end result is of course to prove that we can use the compound and wait till it selectively binds to bacterial efflux pumps (we think that's where it's binding), then turn on a flashlight and get a huge selective killing.

Solar radiation is cool too, I guess, just not my cup o' tea. I like to work with the stuff that kills people ;).

well thank you both for the input and especially thanks to you haruspex for the equation. Definitely helped a lot. Once we get the power spectrum for our machine, now we can incorporate that equation into a transform of the spectrum to calculate power by wavelength and distance and keep it equal throughout. Controls and such :D Cheers!