A note on efficiency of photon absorption.

The absorption of light in the photosynthetic process is generally believed to occur through the excitation of electrons in organic molecules to higher energy states thereby initiating a series of reactions. Recently an attempt has been made to fix the theoretical minimum quantum requirement at a number higher than that needed to obey the conservation of energy (2, 3). This argument rests on the application of the second law of thermodynamics to the photon absorption process. We wish to point out, however, that application of the second law of thermodynamics to the absorption of a photon by an atom or molecule is not valid, owing to the unique nature of such an interaction. Since the photon does not actually interact weakly with a large number of atoms or molecules but interacts strongly with only one atom or molecule in the case of absorption; those thermodynamic concepts which have been developed for a statistical description of systems having many degrees of freedom cannot be applied to such a single, isolated quantum interaction ( 1 ). The attempt to introduce second law arguments into the treatment of photon absorption is further complicated by the discussion of the temperature of an incoming photon beam with a prescribed energy distribution. Although it is perfectly proper to speak of the temperature of a gas of photons of various energies distributed according to Planck's formula in radiative equilibrium with the walls of the cavity containing them (the so-called black body); the temperature of a single photon of a certain wavelength or of a beam of photons of a certain wavelength or wavelength range is not a definable quantity. One may define a temperature for such a beam in some arbitrary way, but this temperature will vary with the definition and is not really a measure of any physical property of the photon beam. Indeed if one were to give some sort of characteristic temperature to a collimated beam of monochromatic photons, one might ascribe a temperature close to zero for such a wellordered system. This would be in analogy with the problem of a collimated beam of monatomic molecules all having the same velocity (i.e., zero random motion). The more serious objection to the use of the second