Planck’s Black-Body Radiation Formula and Einstein’s Photon

Abstract

In the previous chapter, we saw that the quantum theory of radiation arose because classical physics, as contained in Newton’s laws of motion, in thermodynamics, and in Maxwell’s electromagnetic theory of radiation, cannot correctly describe “black-body” radition, that is, the continuous spectrum of the energy emitted per second from a 1-cm² hole in the wall of a furnace at a given absolute temperature. This spectrum had been studied experimentally for some years before Planck obtained its correct algebraic formula, so that the theoretical physicists, like Planck, who were trying to deduce the formula from first principles knew their goal: to find a formula from which the correct intensity of the emitted radiation at a given frequency for a given furnace temperature can be calculated. This formula for the intensity of the radiation must contain algebraically only the absolute temperature of the furnace and the frequency of the emitted radiation in such a combination that the intensity for a given frequency, as calculated from the formula, agrees with the observed intensity for that frequency.

How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth.

—Sir Arthur Conan Doyle