One family of radiation split into many lines
Manne Siegbahn improved X-ray sources, vacuum technique and spectrographs until characteristic series could be measured more precisely. His Nobel lecture, given in 1925 for the 1924 prize, arranges these lines into energy diagrams. The advance was more than a sharper photograph: the newly separated lines limited which atomic levels could exist.
The lecture compares X-ray and optical series using combination rules: a set of transition energies must fit one common set of level differences. That is a stricter test than giving each visible peak its own energy label.
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A precise angle needs a stable instrument
A dispersing crystal turns wavelength into angle through a chosen reflection. Slit width, crystal quality, goniometer calibration, temperature and source stability all shape the observed line. Extra digits on the angle scale cannot make up for an unresolved doublet or a drifting lattice spacing.
In first order, photon energy is inversely proportional to the plane spacing times the sine of the Bragg angle. The angle is measured from the planes, and the spacing is a calibrated property of the analyzer crystal. Here the crystal is part of the instrument, not necessarily the specimen being studied.
Lines that share a level test the diagram
If two transitions end in the same state, the difference between their photon energies constrains the energy gap between their starting states. Relations that repeat across a series help catch wrong assignments. Fine splittings show that a single shell label does not specify every allowed state of the atom.
The lecture uses the orbital language and notation of its time, and its diagrams should not be read as electrons literally circling like planets. Modern shell, angular-momentum and many-electron theory explains the same spectra in a different framework.
Sources: [2]
Line position and line strength answer different questions
Line positions test energy differences. Intensities also depend on excitation probability, branching, absorption and detector response. A line list can therefore constrain atomic structure without serving as a concentration standard.
The same distinction separates Manne Siegbahn’s photon spectroscopy from Kai Siegbahn’s electron spectroscopy. In an emission experiment the measured energy belongs to a photon; in XPS it belongs to an electron, referenced to the analyzer. Renaming one technique does not make its equations apply to the other.
Sources: [2]
Read the diagrams as a connected network
Start with the optical and X-ray diagrams in the lecture, then trace which measured lines connect the same states. Keep three claims apart: how precise the apparatus was, how the levels were assigned and how modern theory interprets them. The linked microanalysis Lab deals with how detectors tell lines apart; the earlier electron-spectroscopy article follows the different XPS measurement.