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