Moseley's Law

Moseley's Law is an empirical solution for the characteristic x-rays. Moseley used a monochromator and film to calculate the wavelength of characteristic x-rays generated by the elements (13 $<$ Z $<$ 79). He then plotted Z verses $\nu^{0.5}$. He, ``approximated to a straight line,'' the resulting data points and concluded that the two equations (Moseley's Law) accurately described the generation of characteristic x-rays. Months earlier Bohr had published Part I of his paper, On the Constitution of Atoms and Molecules, in which he solves for the Balmer series for hydrogen. Moseley explains his solution in terms of the Bohr atom, and indicates that the constant, $\sigma$, from section 1.2 was a, ``small term a rising from the influence of the n electrons in the ring on each other.'' Further, in 1914, he indirectly indicates that $\sigma$ acted as a shielding mechanism, although he fails to express this directly. He wrote, ``The fact that the numbers and arrangement of the lines in the K and the L spectra are quite different, strongly suggests that they come from distinct vibrating systems, while the face that [$\sigma$] is much larger for the L lines than for the K lines suggests that the L system is situated the further from the nucleus.'' He was correct in that he electron shielding was the cause of $\sigma$, although we've since rejected the Bohr atom, in favor of wave mechanics.

It should be concluded that the $\sigma$ term from Moseley's Law is a crude shielding term, and that the error between the Moseley calculation and the experimental value, is primarily a problem because the shielding term present in Moseley's equation, isn't really constant, although it is approximated to be so. Moseley's work was a break through at the time, but now that we better understand the theory behind binding energy and shielding, we should improve his work as shown in section 3.

Presented are plots showing the misfit of Moseley's Law and experimental values. The plots, figures 6,7, and 8, show $\sqrt{\nu}$ as a function of Z so that Moseley's approximated straight line can be seen as compared to modern data.

Figure 6: Moseley's Law Compared to Experimental Values for K$\alpha$

Figure 7: Moseley's Law Compared to Experimental Values for K$\beta$

Figure 8: Moseley's Law Compared to Experimental Values for L