When X-rays hit matter, they can knock out an inner-shell electron, and another electron falls into the vacant spot, emitting an X-ray of a specific energy. Because that so-called characteristic X-ray energy is unique for each element, measuring the spectrum makes it possible to identify elements. Instrumentation in the 1910s, however, lacked precision; wavelength errors were significant and many gaps between experiment and theory remained. Siegbahn designed a high-resolution crystal spectrometer that operated in vacuum and measured X-ray wavelengths with picometre accuracy, far better than earlier devices. He also introduced the Kα, Lβ style notation—now called the Siegbahn notation—that organized the confusing forest of spectral lines. His data confirmed Moseley’s law and the energy differences predicted by emerging quantum theory, solidifying atomic structure models. Precise X-ray spectroscopy is now a core tool for detecting impurities in alloys and evaluating semiconductor materials in modern analytical chemistry and engineering. It is likewise the basis for determining the elemental makeup of stars and galaxies with space-based X-ray telescopes. The incremental improvements Siegbahn made to instrument design influenced the development of detectors for today’s high-energy physics experiments. This blend of technical innovation and systematic data collection earned him the 1924 Nobel Prize in Physics.

Siegbahn installed a curved-crystal spectrometer arranged on a Rowland circle inside a vacuum chamber and moved the collimator slits and diffraction crystal with micrometre precision, achieving relative wavelength accuracies better than 0.02 %. The K- and L-series wavelength data he collected provided a detailed test of Moseley’s law, in which √(1/λ) varies linearly with atomic number Z, and helped extract empirical formulas for inner-shell shielding. He was the first to resolve what looked like a single Kα line into the doublet Kα₁ and Kα₂, thereby demonstrating fine-structure splitting caused by spin–orbit interaction. These precise spectra served as critical benchmarks during the transition from the Bohr–Sommerfeld model to the Dirac equation, supplying early quantum theorists with rich experimental evidence. The Siegbahn notation (e.g., Kα, Lβ) indicates the initial and final electron shells involved in a transition and remains the standard nomenclature in modern X-ray spectroscopy. His instrument design included innovations such as lead-glass shielding to suppress background and the use of ionization chambers or photomultipliers to improve detection efficiency, balancing safety with sensitivity. His work guided later improvements in the very-soft and high-energy X-ray regimes, leading to wavelength-dispersive spectroscopy (WDS) and the design of monochromatic X-ray sources. Today’s electron probe micro-analysers (EPMA) and high-resolution experiments at synchrotron radiation facilities inherit and extend Siegbahn’s foundational concepts. Moreover, the systematic wavelength tables he compiled remain heavily cited and form the prototype for international X-ray databases such as the NIST X-ray Transition Energies Database. Thus, Siegbahn’s achievements go far beyond instrument building; they continue to influence atomic physics, analytical chemistry, and materials science to this day.

Siegbahn designed a vacuum focusing spectrometer that combined a stable Ag-anode X-ray source with a 120 mm-radius quartz crystal, maintaining the Rowland geometry to achieve a resolving power Δλ/λ ≈ 2×10⁻⁴. His wavelength calibration became the pivotal reference during the transition from transmission grating spectrometers to reflective Bragg geometries and stimulated the development of the Johann and Johansson crystal optics. Systematic measurements of K-series fine structure verified the Z⁴ dependence of the spin-orbit splitting ΔE and quantified its deviation from non-relativistic Hartree calculations. In the L–M multiple transition region he analyzed satellite lines in detail, providing one of the earliest experimental indications of competing Auger de-excitation mechanisms. His absolute wavelength scale (Al Kα = 8.3389 Å) was later inherited by ISO/TC201 X-ray reference standards. Using a mercury-vapor ionization chamber in the detection chain, he implemented low-voltage feedback compensation to extend linear response and achieved S/N = 300 at count rates of 10³ s⁻¹. The subscript system he introduced (α, β, γ, α₁, α₂, etc.) remained compatible with later IUPAC X-ray notation. Preceding modern multilayer mirror analyses, he applied diffraction-intensity corrections based on Si(111) and NaCl(200) structure factors, paving the way for absolute intensity calculations. Such precise experiments simultaneously constrained nuclear charge distribution and inter-shell electron binding energies, serving to validate later atomic models employing many-body perturbation theory (MBPT). Siegbahn’s methodology remains directly relevant to high-brilliance synchrotron and XFEL hard-X-ray inner-shell spectroscopy, forming a cornerstone of modern wavelength metrology.