Help understanding unit: Micromoles per square meter per second

The context is light, illumnination, photons.

The units seem to suggest something different from the definitions I have found:

$$\frac{µmol}{m^2 s}$$

This, to me, says I have one millionth of a mole ($$6.022×10^{17}$$) in photons landing on a one meter square area every second.

However, the definitions I have found pretty much state something similar to the above and then add that the quantity is divided by a mole ($$6.022×10^{23}$$).

Frankly, not sure what that means. Is it meant to represent what fraction of a micro-mole lands on a one square meter per second? I realize mol is unit-less, which might make it confusing.

In other words, you count the photons you have in one second, divide that by Avogadro's number (or is it Avogadro's number divided by 1E6?) and that's your number.

• "mol is unit-less". Is "dozen" unit-less? I recommend thinking of the units of mol as "particles": 1 mol = 6.022x10²³ particles. If you take your micromol/m²/s quantity and multiply by Avogadro's number, 6.022x10²³ particles/mol, you will be left with units of particles/m²/s, which is consistent with your physical intuition. – electronpusher Nov 15 at 21:18
• Right, except the definition indicates you divide by Avogadro's number. This tells me what they are after is a representation of what fraction of $6.022x10^{23}$ we have falling on a square meter per second. The corollary to this question being: Why? Why not simply count particles, in other words, "photos per square meter per second"? Is it in order to avoid dealing with potentially very large numbers? Saying 0.5 micromoles per square meter per second might be more convenient than saying we have 3.011E23 photons per square meter per second. – martin's Nov 15 at 21:31
• I would understand that idea. However, we are talking about micromoles and being told to divide by moles. If what we are after is a fraction we count photons and then divide by moles to get the fraction. Maybe I haven't found the right definition. It seems that we are dealing with raw photons at first but then dividing by a full mole yet stating it as a micromole. Not sure how that happens. – martin's Nov 15 at 21:33
• I'm not sure what the question is here. You seem to have come to the correct conclusion yourself. – Cloudy7 Nov 15 at 22:18
• Well, talking about it is helping formulate a clarification. I would say the current question is more about the step in scale. While the unit is micromoles per square meter per second the definition states that the calculation involves dividing by a mole. If I take that literally it means I am dividing micromoles by moles...and the result is micromoles. Again, I do realize these are unit-less. Yet, this is like saying divide one-tenth-of-a-dozen by a dozen and then call the result N one-tenths-of-a-dozen. I'd love to know where I am wrong. Continuing to research the subject as we speak. – martin's Nov 15 at 22:25

1 mol is defined as Avogadro's number $$6.022\cdot10^{23}$$ and you could count anything using moles. We could count some events happening in a fixed time, for example water molecules flowing through a pipe. If we divide the total count of those molecules by elapsed time we get rate of flow which in this case would measured in $$\frac{mol}{s}$$. If we wanted to change the size of that pipe, rate of flow per area might be handy, which would thus be measured in $$\frac{mol}{s\cdot m^2}$$. This is just one example but there are many more. Also 1 micromole is $$10^{-6}$$ mol.