The question now arises: What are the physical meanings of these constants? There is no difficulty in answering the question so far as k is concerned. It enters the theory of radiation as a factor correlating the entropy associated with the state of a thermodynamical system and the probability of that state, and is, therefore, sometimes termed the entropy constant. It appeared, more or less disguised in the kinetic theories of Maxwell and Boltzmann and in the statistical mechanics of Willard-Gibbs long before Planck began his investigations, and it happens to be identical with the quotient of the gas constant, Now R has the value 8.315X I& ergs per degree centigrade for a gram molecule, therefore we get for N, the number of mole cules in a gram molecule, 6.o6 X This result, which differs only very slightly from that obtained by Planck, is in good agree ment with the number obtained by later and quite different methods and it is very remarkable that it can be arrived at in this way. The quantity of electricity carried by a gram atom of hydrogen or other univalent element in electrolysis is found to be 2.895X 10" e.s.u., and when we divide by 6.06X the number of atoms in a gram atom, we get for the charge on an ion 4.77X e.s.u. Planck arrived at the result 4.67X e.s.u., which may be said to be the earliest reasonably accurate estimate of the elementary ionic charge.
In the early days of the quantum theory, the question : What is the physical meaning of the constant It? was often asked. The question then really meant : What is the interpretation in terms of more familiar physical concepts of the type of atomicity sym bolized by h? If the question is put in this way the answer is that h has no physical meaning. The fact is that the weird type of atomicity which finds its expression in Planck's constant is itself a new physical fact, first disclosed in the early development of the quantum theory and is something which can no more be expressed solely in terms of the older concepts of physics than can the dimensions of, say, a dielectric constant be expressed in terms of those of length, mass and time.
the other hand, however distant the illuminated body may be from the source of light or X-rays, in other words, however low the intensity of the radiation the well-known phenomenon of interference characteristic of waves can still be produced. The reconciliation of these two aspects of the phenomenon, namely the independence of the energy of the ejected photo-electrons of the intensity, on the one hand, and the wave character of the radiation on the other, constitutes one of the most formidable problems which physical science has ever encountered. The former of these features seems to require that the radiation is corpuscular in character, while the latter seems to require that it is undulatory and spreads out continuously in all directions.
Recent developments of the quantum theory, more especially the wave mechanics of de Broglie and Schroedinger, suggest the solution of this problem, but meanwhile we shall confine our attention to the historically important explanation of photo electric phenomena which we owe to Einstein, who about the year 1905 suggested that light is propagated through space in the manner of a corpuscular radiation, each corpuscle (or light quan tum) having the energy hv. While this hypothesis frankly ignores those phenomena, such as interference, which have an indubitably undulatory character ; it has the merit of explaining the facts of photo-electricity and allied phenomena. When a light quantum falls on a metal plate, the whole of its energy by may be given up to an electron. Part of this energy, 4, is used up in dragging the electron away from the metal and the rest is retained by the electron as kinetic energy ; so that The quantity 4) is called the work function and is characteristic of the illuminated material. If the incident radiation has a frequency such that the energy is just sufficient to drag the electron out, so that its kinetic energy is zero, then with lower frequencies than it is clear that no electrons can be ejected at all. Equation (24) has been verified experimentally and the constant h contained in it found to be identical with the h in Planck's radiation formula within the limits of experimental error. When very high frequencies are involved, e.g., those of X-radiation by is so large that equation (24) becomes practically and if we consider the converse phenomenon, i.e., the excitation of X-rays by bombarding a metal with electrons, we should expect the highest frequency of the excited X-rays to be given by this equation, or by if V represents the drop of potential between the cathode and anti-cathode and e the electronic charge. This has been verified by Duane. X-radiation of lower frequency than that given by (25) can in general be excited, because the colliding electron may lose part of its energy in causing changes in the electronic constitution of the atoms with the consequent emission of X-radiation characteristic of the material bombarded.