A second qualitative result is that, since the mass of the light-quanta, as defined above, is even for the hardest -rays (), of the order of a tenth of the mass of the electron, it is impossible from the laws of elastic impact that it transfer more than a small part of its energy to it. In other words, if Compton’s assumptions are correct, the photo-electric effect, in which there certainly is such a complete transfer, cannot possibly represent the interaction between a light-wave and a free electron. When the electron is bound in the atom there is no difficulty of this sort, for the huge mass of the atom then permits the momentum equation to be satisfied without forbidding the practically complete transfer of the energy to one of its electrons. From this point of view, then, the photo-electric effect represents the interaction between ether-waves and bound electrons—the Compton effect the interaction between ether-waves and free electrons. The quantitative results which can be deduced from Compton’s assumptions are definite and simple. Combining the energy and momentum equations in the manner shown in Appendix H he obtains easily the result in which represents the increase in wave-length due to the “scattering” of the incident beam by free electrons, and is the angle between the original direction of the beam and the direction at which the scattered waves come to the measuring apparatus. Compton then tested this relation experimentally,[190] using as his incident waves the characteristic -rays from a molybdenum target, and as his scattering substance the free (or substantially free) electrons found in graphite. He found indeed that the -line of molybdenum was shifted toward longer wave-lengths just as predicted, and in approximately the correct amount. There was also an unshifted line presumably due to scattering by bound electrons. Compton had used an ionization-chamber spectrometer for locating his lines. Ross[191] repeated these experiments at Stanford University, California, using the more accurate photographic plate for locating his lines, but still using graphite as the scattering substance. His published photograph shows a line shifted the correct amount and also an unshifted one, but he commented on the fact that the shifted line shows no sign of a separation of the and components while they are clearly separate in the direct picture. [Pg 259]