# Number of particles - dimensional or not?

I think that "number of particles" should be a dimensional quantity, with the same dimension as "amount of substance", because they are only scaled by Avogadro's constant, which then should be dimensionless.

For instance, an electron in an hydrogen atom has an energy of $-2,18 \times 10^{-18} \:\text{J}$. Then, the ionization energy should be $2,18 \times 10^{-18} \:\text{J atom}^{-1} = 1312 \:\text{kJ mol}^{-1}$. Nevertheless, the standard is to consider the first one as plain joules, without the "amount" dimension.

Is there any reason behind this, and by consequence the dimensional character of $N_A$?

• Possible duplicate: Why is the mole/“amount of substance” a dimensional quantity? – lemon Nov 13 '16 at 16:28
• I have already read that before. It didn't answer my doubt, because I understand why moles are dimensional, I just think that "atoms"/"molecules"/etc. should be considered dimensional too, and by consequence $N_A$ would be dimensionless. – J. C. Nov 13 '16 at 16:39

• Sorry my question was not very clear. What matters here is not the Avogadro constant itself, but the "number of particles". If a mole of atoms has dimension N (amount), then $\frac{1}{6.022 \times 10^{23}} \text{mol}$, which corresponds to a single particle, should also have dimension N. The number of particles is a multiple of this, so it should be of dimension N too, from my point of view. – J. C. Nov 13 '16 at 18:13
• @Joa0 - The number of particles is only secondary to the mole. This number was later added to the mole. You can, of course, define particle number via the mole. The comparison is not like between $kg$ and $g$, it is more like between the unit of capacitance farad ($F$) in the SI system as compared to the unit $cm$ (for capacitance) in the Gauss system. – freecharly Nov 13 '16 at 19:12