124 A SYSTEM OF PHYSICAL CHEMISTRY has been found that the photo-electric effect increases proportionally to this intensity, because the number of electrons emitted increases in the same proportion. As long, however, as the frequency of the light is maintained constant, the velocity of the electrons is also constant. On the other hand, working with constant intensity of light but varying the quality or it frequency has been found that, on increasing the frequency of the light, the photo-electric effect increases, because the to Lenard and speed of the electrons is now increased. According Ladenburg, when the wave-length is thus shortened (at constant in- tensity), the velocity of the electrons emitted increases proportionally to the It is frequency. now known that the square of the is speed proportional to the frequency of the incident light. Below a certain wave-length or frequency, known as the threshold wave-length, the normal photo-electric effect is not observable. That is, with wavelengths longer than a certain value Aq— characteristic of the substance under examination— no electrons are emitted. Hughes has determined the value of Xq for a number of substances, using fresh surfaces, obtained by distillation of the substance in vacuo. These values are given in the following table :— Normal Photo-electric Effect. Threshold Wave-lengths (Xq). Substance.
THE PHOTO-ELECTRIC EFFECT 125 Camb. Phil. Soc, 14, 421, 1908): The [radiant] energy travelling outwards [from the radiating source] with the wave is not spread uniformly over the wave front, but is concentrated on those parts of the front where the pulses are travelling along the lines of force ;'^ these parts correspond to the bright specks, the rest of the wave is thus collected to the dark into isolated ground. . . . The energy regions, these regions being the portions of the lines of force occupied by the pulses or wave motion. In fact, from this point of view, the distribution of energy is very like that contemplated on the old emission theory, according to which the energy was located on moving particles, sparsely disseminated throughout space. The energy is, as it were, done up into bundles, and the energy in any particular bundle does not change as the bundle travels along the line of force. Thus, when light falls upon a metal plate, if we increase the distance of the source of light, we shall diminish the number of these different bundles or units falling on a given area of the metal, but we shall not diminish the energy in the individual units ; thus any effect which can be produced by a unit by itself, will, when the source of light is removed to a greater distance, take place less frequently it is true, but when it does take place it will be of the same character as when the intensity of the light was stronger. This is, I think, the explanation of the remarkable result discovered by Lenard, that though the number of corpuscles emitted by a piece of metal exposed to ultra-violet light increases [as intensity increases], the velocity with which individual corpuscles come from the metal does not depend upon the intensity of the light. this result stood alone, we might suppose that it indicated that If the forces which expel the corpuscles from the metal are not the electron forces in the light wave incident on the metal, but that the corpuscles are ejected by the explosion of some of the molecules of the metal which have been put into an unstable state by the incidence of the light ; if this were the case the velocity of the corpuscle would be determined by the properties of the atom of the metal, and not by the intensity of the light, which merely acts as a the trigger explosion. Some experiments made quite recently by to start Dr. E. Ladenburg make, however, this last explanation exceedingly improbable. Ladenburg has investigated the velocities of corpuscles emitted under the action of ultra-violet light of different wave-lengths, and finds that the velocity varies continuously with the frequency ; according to his interpretations of his experiments, the velocity is directly proportional to the frequency.^ Thus, though the velocity of the corpuscles is independent of the intensity of the light, it varies in apparently quite a continuous way with the quality of the light this would be ; very improbable if the corpuscles were expelled by an explosion of the molecule. 1 Thomson assumes that the ether has disseminated through it discrete lines of electric force, these being in a state of tension. The light consists of transverse vibrations travelling along these lines. ^ As already stated, the evidence now available goes to show that the square of the velocity of the electron is proportional to the frequency of the light.