How to write 'number of ...' in a unit?

Question

Q: Which unit is attached to 'number of particles per volume' (e.g. of the atmosphere)? The questions focuses on the 'number of' and not on the 'volume'.

The units [#/m³], [particles/m³] and [1/m³] are used in publications. Neither [#/m³] nor [particles/m³] are SI compliant. However, [1/m³] would be SI compliant but it looks ... incomplete.

edit 1: The particles are of different size and composition. Converting the number of particles into another unit is not reasonable for my application.

I'm voting to close this question as off-topic because it's not about academia. — 410 gone, Mar 21 '16 at 16:10
Thank you @JanDoggen for the suggestion. The particles are of different size and composition. Giving them in mole is not reasonable in this situation. — daniel.heydebreck, Mar 21 '16 at 16:18
In my experience $[m^{-3}]$ or $[cm^{-3}]$ is perfectly reasonable and well understood in the literature. — AtmosphericPrisonEscape, Mar 21 '16 at 16:29
There's nothing wrong with particles per unit volume. However, if the number of particles is very large (e.g., $10^{26}$ particles per unit volume), it would be better to use number of moles rather than number of particles. — David Hammen, Mar 21 '16 at 20:41
@DavidHammen, yes and the fact that "The particles are of different size and composition." does not get in the way. A mole is in fact a unitless quantity, $6.022 \times 10^{23}$, and often applied to mixed gases, liquids and amorphous solids where the definition of "particles" is clear. — Eubie Drew, Mar 21 '16 at 21:46
@AtmosphericPrisonEscape if you put that as an answer, I'd upvote it. — Semidiurnal Simon, Mar 22 '16 at 14:13

AtmosphericPrisonEscape · Accepted Answer · 2016-03-22T15:09:00.587

In my experience $[m^{-3}]$ or $[cm^{-3}]$ as number density is very well understood throughout the communities of both earth, solar-system as well as exoplanetary scientists.

Take for example the recently published The atmosphere of Pluto as observed by New Horizons which in fig. 3 shows the derived atmospheric composition of Pluto from occultation measurments in $[cm^{-3}]$ with some model curves:

(Property of G. R. Gladstone et. al 2016 and the New Horizons Science team)

The density in this unit is just a very natural and convenient outcome of the used occultation-inversion techniques. Thus of course the units are sometimes simply the result of the context in which a work is done, and as other commentators stated, a mole could be used. However I'd argue that $[cm^{-3}]$ is sufficiently simple to be understood in any context and adding moles just makes things unnecessary confusing as it suggests numbers to have a unit, which they don't.
It just physically makes no sense.

How to write 'number of ...' in a unit?

1 Answers1