We want to calculate probability distribution function of distance to the nearest neighbor (NN) particle. (The problem was first considered by Paul Hertz ; for a modern derivation see, e.g.,.) Let us assume N particles inside a sphere having volume V , so that n = N / V . Note that since the particles in the ideal gas are non-interacting, the probability of finding a particle at a certain distance from another particle is the same as the probability of finding a particle at the same distance from any other point; we shall use the center of the sphere.