Precision X-ray emission spectroscopy turns closely spaced spectral lines into quantitative constraints on atomic energy levels. Bragg's law makes a crystal an angular ruler for wavelength: resolving nearby directions can reveal components hidden inside an apparently single line. Accurate line positions and the ability to separate two lines are related, but distinct, experimental achievements.
Karl Manne Georg Siegbahn received the 1924 Nobel Prize in Physics; his lecture was delivered on 11 December 1925.[ref]
The Barkla characteristic X-ray experiment distinguished element-dependent K and L groups through absorption and excitation. Moseley's law related corresponding line frequencies across chemical elements to atomic number. Measuring the components within those groups asks a further question: which distinct atomic energy differences produce the neighbouring spectral lines?
Siegbahn's lecture organizes measured spectral lines into energy levels and resolved double levels.[ref] The payoff is a map of atomic energy differences as well as an element's position in the periodic table.
X-ray emission spectroscopy studies the frequency spectrum of emitted X-rays. The spectral line positions identify electronic energy differences; their strengths also depend on excitation, photon absorption inside the sample, geometry and detector response. An X-ray tube may excite a sample with Electrons, while X-ray fluorescence uses incident photons. The distinction matters when choosing what the experiment measures: identifying a chemical element from a line position is different from determining its abundance from a line strength.