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===Photoelectron spectroscopy=== {{Main|Photoemission spectroscopy|Angle-resolved photoemission spectroscopy|X-ray photoelectron spectroscopy}} [[File:ARPES setup - ultraviolet source - sample holder - electron analyzer.svg|thumb|[[Angle-resolved photoemission spectroscopy]] ([[Angle-resolved photoemission spectroscopy|ARPES]]) experiment. Helium discharge lamp shines ultraviolet light onto the sample in ultra-high vacuum. Hemispherical electron analyzer measures the distribution of ejected electrons with respect to energy and momentum.|alt=]] Because the kinetic energy of the emitted electrons is exactly the energy of the incident photon minus the energy of the electron's binding within an atom, molecule or solid, the binding energy can be determined by shining a [[monochromatic]] [[X-ray]] or [[Ultraviolet|UV]] light of a known energy and measuring the kinetic energies of the photoelectrons.<ref name="Stefan2003" /> The distribution of electron energies is valuable for studying quantum properties of these systems. It can also be used to determine the elemental composition of the samples. For solids, the kinetic energy and emission angle distribution of the photoelectrons is measured for the complete determination of the [[electronic band structure]] in terms of the allowed binding energies and momenta of the electrons. Modern instruments for angle-resolved photoemission spectroscopy are capable of measuring these quantities with a precision better than 1 meV and 0.1Β°.{{citation needed|date=November 2023}} [[Photoelectron spectroscopy]] measurements are usually performed in a high-vacuum environment, because the electrons would be scattered by gas molecules if they were present. However, some companies are now selling products that allow photoemission in air. The light source can be a laser, a discharge tube, or a [[synchrotron radiation]] source.<ref name="Ref_aa">{{cite journal|title=Solid-State Photoelectron Spectroscopy with Synchrotron Radiation|doi=10.1126/science.206.4415.151|year=1979|last1=Weaver|first1=J. H.|last2=Margaritondo|first2=G.|journal=Science|volume=206|issue=4415|pages=151β156|pmid=17801770|bibcode=1979Sci...206..151W|s2cid=23594185}}</ref> The [[Hemispherical electron energy analyzer|concentric hemispherical analyzer]] is a typical electron energy analyzer. It uses an electric field between two hemispheres to change (disperse) the trajectories of incident electrons depending on their kinetic energies.
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