In actual practice no body is absolutely black. Even a body coated with lampblack reflects about 10 per cent. of the light waves incident on it. The Danish physicist Christiansen remarked long ago that a real black body could be produced only if an arrangement could be made whereby the incident waves could be reflected several times in succession before finally being emitted. To take the case of lampblack, three such reflections would reduce the re-emission from the lampblacked body to only ⁴/₁₀₀₀ of the radiation initially falling on it. This type of black body was finally realized by making a cavity in an oven having as its only opening a very small peep-hole, and keeping the temperature of the wall of the oven uniform. If a ray is sent into the cavity through the peep-hole, it will become, so to speak, captured, because, when once inside it will suffer countless reflections from the walls of the cavity, having more and more of its energy absorbed at each reflection. Very little of the radiation thus entering will ever get out again, and consequently such a body will act very much like a “perfect black body” according to the theoretical definition above. Accordingly, the radiation which is emitted from such a glowing cavity through the peep-hole will be black or practically black radiation.
The cavity itself will be criss-crossed in all directions by radiation emitted from one part of the inner surface of the cavity and absorbed by (and partially reflected from) other parts of the surface. When the walls of the cavity are kept at a fixed and uniform temperature there will automatically be produced a state of equilibrium in which every cubic centimetre of the cavity will contain a definite quantity of radiation energy, dependent only on the temperature of the walls. Further, in the equilibrium state the radiation energy will be distributed in a perfectly definite way (dependent as before on the temperature only) among the various types of radiation corresponding to different wave-lengths and frequencies. If there is too much radiation of one kind and too little of another, the walls of the cavity will absorb more of the first kind than they emit, and emit more of the second kind than they absorb, and so the state will vary until the right proportion for equilibrium is attained.
This distribution of the radiation over widely differing wave-lengths can be investigated by examining spectroscopically the light emitted from the peep-hole in the cavity. Then, by means of a bolometer or some other instrument, the heat development in the different portions of the spectrum can be measured. At a temperature of 1500° C., for example, one will find that the maximum energy is represented for rays of wave-length in the close vicinity of 1·8 μ, i.e. in the extreme infra-red. If the temperature is raised, the energy maximum travels off in the direction of the violet end of the spectrum; if the temperature is lowered, it will move farther down into the infra-red.
It is also possible to make a theoretical calculation of the distribution of energy in the spectrum of the black-body radiation at a given temperature. But the results obtained do not agree with experiment. The English physicists, Rayleigh and Jeans, developed on the basis of the classical electrodynamic laws and by apparently convincing arguments a distribution law according to which actual radiation equilibrium becomes impossible, since if it were true the energy in the radiation would tend more and more to go over to the region of short wave-lengths and high frequencies, and this shifting would apparently go on indefinitely. The theory thus leads to results which are not only in disagreement with experiment, but which must be looked upon as extremely unreasonable in themselves.
Planck, however, had vanquished these difficulties and had obtained a radiation law in agreement with experiment by introducing an extremely curious hypothesis. Like Lorentz, he thought of radiation as produced through the medium of small vibrating systems or oscillators, which could emit or absorb rays of a definite frequency ν. But while, according to the Lorentz theory and the classical electrodynamics, radiation can be emitted in infinitely small quantities (i.e. small without limit), Planck assumed that an oscillator can emit and absorb energy only in certain definite quantities called quanta, where the fundamental quantum of radiation is dependent on the frequency of the oscillator, varying directly with the latter. If thus we denote the smallest quantity of energy which an oscillator of frequency ν can emit or absorb by E, then we can write
E = hν,
where h is a definite constant fixed for all frequencies. Accordingly the cavity can receive radiation energy of frequency ν from the radiating oscillators in its wall, or transfer energy to these in no smaller quantity than hν. The total energy of that kind emitted or absorbed at any given time will always be an integral multiple of hν. Oscillators with a frequency 1½ times as great will emit energy in quanta which are 1½ times larger, and so on.
The quantity h is independent, not only of the wave-length, but also of the temperature and nature of the emitting body. This constant, the so-called Planck constant, is thus a universal constant. If one uses the “absolute” units of length, mass and time ([see table, p. 210]), its value comes out as 6·54 × 10⁻²⁷. For the frequency 750 × 10¹² vibrations per second, corresponding to the extreme violet in the visible spectrum, the Planck energy quantum thus becomes about 5 × 10⁻¹² erg, or 3·69 × 10⁻¹⁹ foot-pounds (note that the “erg” is the “absolute” unit of work, or the amount of work done when a body is moved through a distance of 1 cm. by a force of one dyne acting in the direction of the motion, while the “foot-pound” is the work done when a force of 1 pound moves a body 1 foot in the direction of the force). For light belonging to the red end of the spectrum, the energy is about half as great. If we pass, however, to the highest frequencies and the shortest wave-lengths which are known, namely those corresponding to the “hardest” (i.e. most penetrating) γ-rays ([see p. 78]), we meet with energy quanta which are a million times larger, i.e. 2 × 10⁻⁶ erg, although they are still very small compared to any amount of energy measurable mechanically.
This remarkable theory of quanta, which in the hands of Planck still possessed a rather abstract character, proved under Einstein’s ingenious treatment to have the greatest significance in many problems which, like heat radiation, had provided physicists with many difficulties. For by assuming that energy in general could only be given up and taken in in quanta, certain facts about the specific heats of bodies could be accounted for—facts which the older physics had proved powerless to explain. The Planck energy quanta, as Einstein showed, could also explain in a very direct and satisfactory way the photoelectric effect, as it is called. This effect consists in the freeing of electrons from a metal plate which ultra-violet rays are allowed to strike. The maximum velocity with which these electrons are propelled from the plate is found to be independent of the intensity of the incident light, but dependent simply on the frequency of the radiation. Careful measurements have indeed shown, as Einstein predicted, that the incident light really does utilize an energy quantum hν to free each electron and give it velocity ([cf. p. 172]). Of the different methods which nowadays are at hand, the photoelectric effect constitutes one of the best means of determining the value of h. It has been applied for that purpose by Millikan, to whose ingenious experiments the most accurate direct determination of h is actually due.
All this lay completely outside the laws of electrodynamics, and pointed to the existence of unknown and more fundamental laws. But, for the time being, physicists had to be satisfied merely with a recognition of the fact that these mysterious energy quanta play a very significant part in many phenomena.