# How to write 'number of …' in a unit?

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
• Where would you suggest to ask this question instead? – daniel.heydebreck Mar 21 '16 at 16:15
• Mole? My chemistry/physics is a bit rusty... – Jan Doggen Mar 21 '16 at 16:15
• In my experience $[m^{-3}]$ or $[cm^{-3}]$ is perfectly reasonable and well understood in the literature. – AtmosphericPrisonEscape Mar 21 '16 at 16:29
• @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

## 1 Answer

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.