Range of 1-10 kev Electrons in Solids

The range of 1-10 kev electrons in metals and phosphors has been measured by recording the light output as a function of energy from a sample consisting of a metallic layer deposited on a transparent phosphor layer. The measurements lead to the development of the following range-energy expression: $R=250\left(\frac{A}{\rho Z^{\frac{n}{2}}}\right)E^n,$ where $n=\frac{1.2}{(1-0.29\mathrm{}{log}_{10}Z)}$, $E=\mathrm{energy}\mathrm{in}\mathrm{kev}$, $R=\mathrm{range}\mathrm{in}\mathrm{angstroms}$, and $A$, $\rho$, $Z$, have their customary meaning. This differs from the usual range expression in the dependency of $n$ on $Z$. Usually $n$ is assumed to be independent of material. This dependency can be justified on the basis of Bethe's theory of electron stopping power.