Quantum theory of the recoil of electrons from scattered x-rays.—This is an extension of the quantum theory of scattering suggested by Compton, which assumes that each directed x-ray quantum is scattered by a single electron. Expressions for the distribution of recoil velocities, of energies and of ranges are developed for each of two postulates, assuming (1) the scattered radiation consists of directed quanta, and (2) the scattered radiation proceeds as spherical waves. On the first postulate the maximum recoil energy is shown to be $E_m=h{\nu }_0\times \frac{2\alpha }{(1+2\mathrm{}\alpha )}$, where $\alpha =\frac{h}{\mathrm{mc}{\lambda }_0}$; the recoil electrons are shown to be concentrated at angles near the direction of the primary beam; and from the distribution of energy, using a relation given by C. T. R. Wilson, the distribution of ranges is found to be such that two-thirds have tracks shorter than half the maximum range. The maximum range increases rapidly with frequency. The values for the maximum ranges in the case of x-rays (.34 to.48 A) are computed to be about one-third of those observed by Wilson for his fish tracts, but the difference may be due to the lack of homogeneity of the rays used. The relative number of recoil electrons to photo-electrons increases with the frequency and is in agreement with observations by Wilson. The second postulate, however, leads to a value for $E_m$ only one-fourth that given above, a value which is inconsistent with that derived from a consideration of radiation pressure and which leads to values for maximum ranges one-fiftieth of those observed by Wilson. Other experimental observations are cited which also lead to the conclusion that the first postulate is much more likely to be true than the second, hence, that each quantum of scattered radiation is probably emitted in a definite direction.

• Received 25 October 1923

DOI:https://doi.org/10.1103/PhysRev.23.439