It follows therefore that the maximum energy of the electrons ejected by radiation of frequency v is hP—P, where P represents any work that has to be done in removing the electron from the place where it absorbs to the place where it is observed. We may subdivide this further and write w for the work to remove the electron just clear of the atom, and P' for the work to remove the electron clear of the body as a whole. These quantities w and P' have different values and importance according to the region of wave-length concerned. P', the work to remove the electron clear of the body, is intimately connected with the work function occurring in Richardson's thermionic equation, and is negligible except in the case of visible light. The quantity w is far more interesting, and depends on the particular position in the atom from which the electron comes. It is a true atomic con stant. Up to a certain point we may imagine the electrons in the atom to be arranged in shells, each shell characterized by a cer tain energy. To remove an electron from a shell and merely to bring it outside the atom with a vanishingly small energy will require the expenditure of a certain characteristic amount of work, w1, w2, w3, etc., according to whether the electron comes from the first, second or third shell. We see, therefore, that on Einstein's hypothesis, light of frequency v incident on a collec tion of such atoms would liberate several groups of electrons of different energies: but that the innermost shells would be untouched if the energy of the quantum by were less than the characteristic energies of the shells etc.
It only remains now to write down the expression for the energy of the electron in order to obtain Einstein's famous equation. For low velocities this may be written but for high veloci ties near that of light the correct relativity expression must be used. This is where m is the mass of the electron, c the velocity of light in vacuo, and (3 the velocity of the electron. It is frequently con venient to express this energy by giving the potential fall in volts V an electron 13 must pass through in order to acquire this en ergy. Then, if e is the charge on the electron in electrostatic units and since 30o volts equal one electrostatic unit of potential, we have finally The equation as written here is more explicit than that originally given by Einstein, and considerable research was needed to estab lish it, but essentially it was all implied in the original paper. The succeeding sections indicate the main steps by which this predic tion was shown to be true and how its details were elucidated.
was seven years after Einstein had shown his theory agreed in its general lines with Lenard's experiments before it was established definitely by 0. W. Richardson, K. T. Compton and also A. L. Hughes that the energy of the emitted electron did increase pro portionately with the frequency, and that the constant of propor tionality was approximately equal to the value of Planck's con stant h obtained by other means. Subsequently Millikan carried out an extensive research which established the relation so accu rately that it is now considered to give one of the most trust worthy values for h. This method is typical of the best method of investigation of the photoelectric effect of light and will be de scribed in some detail. The apparatus is shown in fig. 1, and may conveniently be considered in two parts, as divided by the dotted line. Cast cylinders of the alkali metals (sodium, potassium, lith ium) were mounted on an axle in a highly evacuated glass vessel. The actual experiment is carried out by the part of the apparatus to the right of the dotted line, light entering through the window, and falling on the metal surface. Previous work had shown that reliable results could be obtained only when the metal had a clean, fresh surface prepared in vacuo, and the apparatus on the left of the dotted line consisted of various devices by which the cylinder of alkali metal could be brought opposite the knife, which was then operated by an electromagnet outside the tube so as to shave off the outer layer of the alkali metal, leaving a fresh un contaminated surface. Supposing this to be done the cylinder was then rotated to be opposite the window and the actual experi ment could begin. A beam of monochromatic light from a spec trometer passed through the window and fell on the prepared surface, leading to the emission of electrons which were collected by the gauze cylinder, on the right side of the apparatus, con nected to a quadrant electrometer. If a small positive potential were then applied to the metal block, the electrons would arrive at the gauze with lower energies, owing to the retarding action of the potential. The maximum energy of emission could thus be measured by finding that positive potential V which just sufficed to prevent any electrons arriving at the gauze and communicating their charge to the quadrant electrometer. The maximum energy of the electrons is then Ve, where e is the electronic charge. Millikan showed to an accuracy of one half of 1% that, with each metal, the energy of the emitted electrons varied linearly with the frequency of the light, and that in each case the constant of pro portionality was the same, and equal, within the experimental error, to the values obtained for Planck's constant by other methods.