I call attention to several errors in a recent article by Vollmer1 that invalidate his explanation for how the line spectrum of atoms is transformed into the continuous spectrum of thermal radiation. Following Einstein’s 1916 derivation2 of Planck’s black-body formula, the transformation of this line spectrum to thermal radiation at discrete frequencies associated with these transitions has been discussed often, particularly in the astronomy literature.3 But the question of how discrete atomic transitions can give rise to black-body radiation that is continuous in frequency has been ignored. To fill this gap, I present here a novel derivation of this transformation in a model of a hot gas of atoms with only two energy levels.

Vollmer’s arguments are based on Einstein’s original model of stationary atoms,2 but with only two energy levels corresponding to an excited state and a ground state, which are in thermal equilibrium with...

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