2.5.3.5. Moseley's Law

Henry Moseley discovered that the wavelength (energy) of an X-ray depended upon the nuclear charge of an atom. In 1913, working at the University of Manchester, he photographed the X-ray spectrum of 10 elements that occupied consecutive places in the periodic table. He concluded that there was "a fundamental quantity which increases by regular steps as we pass from one element to the next." In 1920, Rutherford at Cambridge identified this quantity as the atomic number. The Ka lines shifted to higher energy with increased atomic number because the inner-shell electrons are more tightly bound by the higher number of protons in the nuclei (Figures 2.5.3.5a and 2.5.3.5b). The energy of transition is proportional to the number of shells changed; Ka radiation is less energetic than Kb.

	Figure 2.5.3.5a. Energies of major X-ray emission lines observed below 10 keV.
Figure 2.5.3.5b. Moseley's relation between wavelength and atomic number for the Ka1, La1 and Ma1 spectral lines (after Goldstein et al. 1981).

Moseley's Law describes the relationship between atomic number and wavelength of a spectral line:

 

The constant σ (sigma) is equal to 1 for the K-lines and 7.4 for the more shielded L-lines. For energy this expression is approximately equivalent to:

Moseley's determination of this relationship provided a simple test of the order of the elements according to Z. It showed where elements were missing from the periodic table and led to the discovery of some of these elements. For example, hafnium (Hf), which chemically is almost identical to zirconium (Zr), was identified by D. Coster and G. von Hevesy in 1923 from its X-ray spectrum.

If the impinging electrons are insufficiently energetic to excite Ka radiation for a given element, they can excite La or Ma radiation, which require less energy to produce. This means that the excitation potentials (E_c) are higher for K-lines than L-lines or M-lines (see table below). Data for all elements may be found at http://physics.nist.gov/PhysRefData/XrayTrans/Html/search.html,  http://xray.uu.se/hypertext/XREmission.html (most K- and L-lines) and http://www.csrri.iit.edu/periodic-table.html (absorption edges and α and β lines). For a given element, the energy of K radiation is greater than L radiation, which is, in turn, greater than M radiation. For example, E_c for Fe-Ka is 7.11 keV, whereas E_c for Fe-La is 0.71 keV. Thus, incident electrons of 5 keV energy, will not excite Fe-Ka, but can excite Fe-La. Often in analysis, one can use L-lines if K-lines are too energetic to excite efficiently; however, the peak-to-background ratio is not as good for L-lines and M-lines as for K-lines.

X-RAY & ABSORPTION EDGE ENERGIES (keV)

Copyright 1997-2003, James H. Wittke

Last update: 01/18/2006 01:47 PM.