# Boltzmann-photons

01 Oct 2014Can you estimate what fraction of photons in a Planck-spectrum are described by classical Boltzmann-statistics?

It’s fair to say that the high-energy part of the photon spectrum obeys classical Boltzmann-statistics and that in the low-energy part quantum statistics plays a role, specifically Bose-Einstein statistics. A good choice for separating the two regimes is the maximum of the Planck-curve which is given by Wien’s displacement law. Integrating the number density of the spectrum up from the maximum of the curve to infinity and normalising by the total number of photons yields a number in the vicinity of \(1/2\).