Theory of the Number of Beta-rays Associated with Scattered X-rays

Abstract

In a recent paper by Compton and Simon the ratio of the number of recoil electron tracks to that of photo-electron tracks has been found equal to the ratio of scattering coefficient $\sigma$ to true absorption coefficient $T$ for short wave-length x-rays, as predicted by Compton and Hubbard, but for long wave-lengths the experimental ratio is distinctly smaller. In the present paper a correction factor is applied to $\frac{\sigma }{T}$ by taking into account the motion and the binding energy of the scattering electron in its Bohr orbit and also the minimum energy which the recoil electron must have in order to produce a visible track in a Wilson cloud apparatus. Assuming a minimum energy of 630 volts for a recoil electron to produce a visible track, the correction factor for a primary wave-length of 0.71A is 0.36, thus making the theoretical value of the ratio of recoil to photo-electron tracks 0.097 as against an experimental value of 0.10. For other wave-lengths the agreement is equally good.