A Precision Measurement of the Change of Wave-length of Scattered X-rays

Abstract

According to the quantum theory, the change of wave-length due to scattering is $\delta \gamma =\left(\frac{h}{\mathrm{mc}}\right)$ $(1-cos\phi )$ where $h$ is the radiation constant, $m$ the mass of an electron, $c$ the velocity of light and $\phi$ the angle of scattering. In the present experiments $\phi$ was made as large as possible (169°) by placing the slits and calcite crystal in a lead box fastened to the Coolidge tube. Mo $\mathrm{K}\alpha$ and $\mathrm{K}\beta$ radiation was scattered from paraffin back to the crystal and then to a photographic plate; Zr $\mathrm{K}\alpha$ rays for comparison were obtained from a Zr radiator. The best plate required an exposure of 48 hr. The change of wave-length was measured 16 times by means of a special microphotometer. After certain corrections were made, the shift came out (.04825 ±.0002)A; the theoretical value is.04798 ±.0001. This agreement is an excellent confirmation of the theory. This effect may also be used to obtain a measurement of $m$ which is independent of $\frac{e}{m}$. The value of the mass of the electron thus computed from these measurements is (8.99 ±.034) × ${10}^{-28\mathrm{}}$ gm in agreement with the mean result from deflection experiments, whereas the spectroscopic value of $\frac{e}{m}$ gives 9.04.