*hohlraum*(hollow space). The waves themselves carry energy that is continually being exchanged with the energy of atoms in the walls, and the problem Planck set out to solve was how to explain the way in which all the available energy was distributed—some of it in the walls, some of it in the radiation, with that in the radiation divided among waves of different frequencies. This is a complex system with a vast number of atoms and infinitely many wavelengths. Planck found that he could account for the observed behavior of this system and successfully explain how the available energy is shared among the various parts of the system only if he postulated that energy could be transferred from matter to radiation in bundles of a certain size, given by the equation

*E = hf *,

where *E *is the energy in one bundle of radiation—or one photon, as we would say now—and *f *is the frequency of the radiation. Actually Planck thought only in terms of quantized energy exchange, not in terms of quantized radiation. He continued to believe in a continuous pool of radiant energy.^{1} By adjusting the numerical value of his new constant *h *to get the best agreement between the calculated and measured distribution of energy among different wavelengths, Planck was able to determine *h *to an accuracy of about 2%.

Einstein took the second radical step. He assumed that the quantum bundle of energy, after being transferred from matter to radiation, retained its quantum identity, behaving as an identifiable “particle” of light (later to be called a photon) that could be reabsorbed by matter only as a whole unit or not at all. Einstein realized that this granular concept of electromagnetic radiation could account beautifully for a different and very much simpler phenomenon than the one studied by Planck. Planck had considered a system composed of a vast number of atoms and, as we know now, a vast number of photons; Einstein considered an experiment involving the elementary event of the absorption of a single photon. In this so-called photoelectric effect, a single electron within a solid substance absorbs all the energy of a single photon and springs forth from the surface of the substance, revealing by its kinetic energy how much energy it has absorbed.^{2}

1^{} In fact, Planck never accepted Einstein’s photon idea. When, in 1913, Planck and several of his colleagues nominated Einstein for membership in the Prussian Academy of Sciences, it was, they said, despite Einstein’s having “overshot the target . . . in his light quantum hypothesis,” which, in light of his other achievements, “should not be held too much against him.”

2^{} The escaping electron is pulled backward by the surface of the substance it is leaving, so that its final kinetic energy is less than the energy it acquired from the photon. This is an effect readily taken into account. It is rather like the gravitational pull on an escaping spacecraft that takes away some of the craft’s energy.