!9
The Light - Quantum
19a. From Kirchhoff to Planck
In the last four months of 1859, there occurred a number of events that were to
change the course of science.
On the twelfth of September, Le Verrier submitted to the French Academy of
Sciences the text of his letter to Faye concerning an unexplained advance of the
perihelion of Mercury (see Section 14c), the effect explained by Einstein in
November 1915. On the twenty-fourth of November, a book was published in
London entitled On the Origin of Species by Means of Natural Selection, or the
Preservation of Favoured Races in the Struggle for Life, by Charles Robert Dar-
win. Meanwhile on the twentieth of October, Gustav Kirchhoff from Heidelberg
submitted his observation that the dark D lines in the solar spectrum are darkened
still further by the interposition of a sodium flame [Kl]. As a result, a few weeks
later he proved a theorem and posed a challenge. The response to Kirchhoff's
challenge led to the discovery of the quantum theory.
Consider a body in thermal equilibrium with radiation. Let the radiation
energy which the body absorbs be converted to thermal energy only, not to any
other energy form. Let E,dv denote the amount of energy emitted by the body per
unit time per cm^2 in the frequency interval dv. Let A, be its absorption coefficient
for frequency v. Kirchhoff's theorem [K2] states that EJA» depends only on v
and the temperature T and is independent of any other characteristic of the body:Kirchhoff called a body perfectly black if A, = 1. Thus J(v, T) is the emissive
power of a blackbody. He also gave an operational definition for a system, the
'Hohlraumstrahlung,' which acts as a perfect blackbody: 'Given a space enclosed
by bodies of equal temperature, through which no radiation can penetrate, then
every bundle of radiation within this space is constituted, with respect to quality
and intensity, as if it came from a completely black body of the same temperature.'
Kirchhoff challenged theorists and experimentalists alike: 'It is a highly impor-
tant task to find this function [/]. Great difficulties stand in the way of its exper-
imental determination. Nevertheless, there appear grounds for the hope that it has
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