Mean inter-particle distance

Mean inter-particle distance (or mean inter-particle separation) is the mean distance between microscopic particles (usually atoms or molecules) in a macroscopic body. In the case of the ideal gas, it is expressed as

$a=\left({\frac {3}{4\pi n}}\right)^{1/3},$

where $n$ is the particle density. Numerically this corresponds to the radius of a sphere having per-particle volume $1/n$. Sometimes in the literature another definition is used, $a=1/n^{1/3}$, corresponding to the length of the edge of the cube with the per-particle volume $1/n$. Evidently, the two definitions differ by a factor of $\approx 1.61$, thus one has to exercise care if an article fails to define the parameter exactly. On the other hand, it is often used in qualitative statements where such a numeric factor is either irrelevant or plays an insignificant role, e.g.,

• "a potential energy ... is proportional to some power n of the inter-particle distance r" (Virial theorem)
• "the inter-particle distance is much larger than the thermal de Broglie wavelength" (Kinetic theory)