The number density (symbol: n or ρN) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.)
The term number concentration (symbol: lowercase n, or C, to avoid confusion with amount of substance indicated by uppercase N) is sometimes used in chemistry for the same quantity, particularly when comparing with other concentrations.
where N is the total number of objects in a volume V. Here it is assumed[2] that N is large enough that rounding of the count to the nearest integer does not introduce much of an error, however V is chosen to be small enough that the resulting n does not depend much on the size or shape of the volume V because of large-scale features.
Column number density is a kind of areal density, the number or count of a substance per unit area, obtained integrating volumetric number density along a vertical path:
In SI units, number density is measured in m−3, although cm−3 is often used.
However, these units are not quite practical when dealing with atoms or molecules of gases, liquids or solids at room temperature and atmospheric pressure, because the resulting numbers are extremely large (on the order of 1020).
Using the number density of an ideal gas at 0 °C and 1 atm as a yardstick: n0 = 1 amg = 2.6867774 × 1025 m−3 is often introduced as a unit of number density, for any substances at any conditions (not necessarily limited to an ideal gas at 0 °C and 1 atm).
where dV = dx dy dz is a volume element.
Similar expressions are valid for electric charge or any other extensive quantity associated with countable objects.
For any substance, the number density can be expressed in terms of its amount concentration c (in mol/m3) as
For atoms or molecules of a well-defined molar mass M (in kg/mol), the number density can sometimes be expressed in terms of their mass density ρm (in kg/m3) as
Note that the ratio M/NA is the mass of a single atom or molecule in kg.
The following table lists common examples of number densities at 1 atm and 20 °C, unless otherwise noted.