Units conversion - quanta/cm$^2$/s and photons/cm$^2$/s

Question

Can you tell me if there is any difference between these 2 units?

$\log \mathrm{quanta/cm^2/s}$ vs $\log \mathrm{photons/cm^2/s}$

Thanks

Photons are a type of quantua. So the latter is more vague/general. — Sean E. Lake, Oct 04 '22 at 15:09

score 0 · Answer 1 · answered Jul 03 '19 at 11:34

0

"Number of photons" and "Number of quanta" are both dimensionless so

"quanta" cm$^{-2}$ s$^{-1}$ has the same units as "photons" cm$^{-2}$ s$^{-1}$.

But strictly, both expressions are wrong since:

$\log{x}= (x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - (1/4)(x-1)^4 + ...$

So the argument inside the logarithm should be unit-less.

answered Jul 03 '19 at 11:34

Gyromagnetic

Note that $\log(a/b)\equiv\log(a)-\log(b)$, so it is possible for units to be present in the argument of logarithms, though care needs to be taken (I believe there is a PSE post on the use of units in log) – Kyle Kanos Jul 03 '19 at 14:33
Relevant posts on why and how logarithms of dimensionful quantities can be made to work: Why is it “bad taste” to have a dimensional quantity in the argument of a logarithm or exponential function?, What is the logarithm of a kilometer? Is it a dimensionless number?, and links therein. – Emilio Pisanty Jan 28 '21 at 13:16

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