A Determination ofemfrom the Refraction of X-Rays in a Diamond Prism

Abstract

Measurements of the index of refraction of the copper $K_{\beta }$ line by a diamond prism have been made with an estimated accuracy of one part in 10,000. These measurements together with the quantum theory of dispersion and the ruled grating wave-length of the copper $K_{\beta }$ line afford a method of evaluating $\frac{e}{m}$ with an accuracy comparable to that of previous determinations by other methods. The value of $\frac{e}{m}$ is given by the equation $\frac{e}{m}=\delta {\left[\frac{{\lambda }^2\rho F}{2\pi W}{\Sigma }_1^s{N}_s\mathrm{}\{1+A\}\mathrm{}\right]}^{-1\mathrm{}},$ where $\delta$, $\lambda$, $\rho$, $R$, $N_s$ and $W$ have their usual meaning and $A$ is the factor which takes into account the electronic binding. For carbon and a ${\lambda }^{2.75}$ law of absorption, the value of the ${\Sigma }_1^s=6.0163\mathrm{}\pm 0.0006$. Using $\delta =9224.4\mathrm{}\times {10}^{-9\mathrm{}}$, $W=12.0148\mathrm{}$, $\rho =3.5154\mathrm{}$, $F=96513.1\mathrm{}$, $\lambda =1.39220\mathrm{}\mathrm{A}$, one obtains $\frac{e}{m}=(1.7601\mathrm{}\pm 0.0003)\times {10}^7$ e.m.u. This bound electron value is higher than most previous spectroscopic determinations but is in excellent agreement with the free electron results of Dunnington.