<p>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.</p>

<p>Take for example the recently published <a href="http://science.sciencemag.org/content/351/6279/aad8866.full" rel="noreferrer">The atmosphere of Pluto as observed by New Horizons</a> which in fig. 3 shows the derived atmospheric composition of Pluto from occultation measurments in $[cm^{-3}]$ with some model curves:</p>

<p><a href="https://i.sstatic.net/Lms3B.jpg" rel="noreferrer"><img src="https://i.sstatic.net/Lms3B.jpg" alt="enter image description here"></a> (Property of G. R. Gladstone et. al 2016 and the New Horizons Science team)</p>

<p>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.<br>
It just physically makes no sense.  </p>

CC BY-SA 3.0
2016-03-22T15:03:04.340Z
2016-03-22T15:09:00.587Z
2016-03-22T15:09:00.587Z
AtmosphericPrisonEscape
<p><strong>Q:</strong> Which unit is attached to '<em>number of particles per volume</em>' (e.g. of the atmosphere)? The questions focuses on the '<strong>number of</strong>' and not on the 'volume'.</p>

<p>The units [#/m<sup>3</sup>], [particles/m<sup>3</sup>] and [1/m<sup>3</sup>] are used in publications. Neither [#/m<sup>3</sup>] nor [particles/m<sup>3</sup>] are SI compliant. However, [1/m<sup>3</sup>] would be SI compliant but it looks ... incomplete.</p>

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

CC BY-SA 3.0
2016-03-21T16:10:58.673Z
I'm voting to close this question as off-topic because it's not about academia.
410 gone
CC BY-SA 3.0
2016-03-21T16:15:40.487Z
Where would you suggest to ask this question instead?
daniel.heydebreck
CC BY-SA 3.0
2016-03-21T16:15:42.837Z
[Mole](https://en.wikipedia.org/wiki/Mole_%28unit%29)? My chemistry/physics is a bit rusty...
Jan Doggen
CC BY-SA 3.0
2016-03-21T16:18:35.793Z
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
CC BY-SA 3.0
2016-03-21T16:29:01.357Z
In my experience $[m^{-3}]$ or $[cm^{-3}]$ is perfectly reasonable and well understood in the literature.
AtmosphericPrisonEscape
CC BY-SA 3.0
2016-03-21T20:41:35.973Z
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
CC BY-SA 3.0
2016-03-21T21:46:36.257Z
@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
CC BY-SA 3.0
2016-03-22T11:05:56.333Z
@DavidHammen and Aabaakawad: Thank you for the replys!
daniel.heydebreck
CC BY-SA 3.0
2016-03-22T14:13:25.143Z
@AtmosphericPrisonEscape if you put that as an answer, I'd upvote it.
Semidiurnal Simon
<atmosphere>
How to write 'number of ...' in a unit?
daniel.heydebreck
# How to write 'number of ...' in a unit?

(Asked by: username_0 on 2016-03-21)

**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.

**Tags:** atmosphere

> **Comments:**
> **username_1**: I'm voting to close this question as off-topic because it's not about academia.  
> **username_0**: Where would you suggest to ask this question instead?  
> **username_2**: [Mole](https://en.wikipedia.org/wiki/Mole_%28unit%29)? My chemistry/physics is a bit rusty...  
> **username_0**: Thank you @username_2 for the suggestion. The particles are of different size and composition. Giving them in mole is not reasonable in this situation.  
> **username_3**: In my experience $[m^{-3}]$ or $[cm^{-3}]$ is perfectly reasonable and well understood in the literature.  
> **username_4**: 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.  
> **username_5**: @username_4, 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.  
> **username_0**: @username_4 and Aabaakawad: Thank you for the replys!  
> **username_6**: @username_3 if you put that as an answer, I'd upvote it.  

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## 1 answers

### Answer by username_3 on 2016-03-22. Score: 7 | Accepted 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](http://science.sciencemag.org/content/351/6279/aad8866.full) which in fig. 3 shows the derived atmospheric composition of Pluto from occultation measurments in $[cm^{-3}]$ with some model curves:

[![enter image description here](https://i.sstatic.net/Lms3B.jpg)](https://i.sstatic.net/Lms3B.jpg) (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.


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