Editing Deuterium (section)

=== Spectroscopy ===
In [[quantum mechanics]], the energy levels of electrons in atoms depend on the [[reduced mass]] of the system of electron and nucleus. For a [[hydrogen atom]], the role of reduced mass is most simply seen in the [[Bohr model]] of the atom, where the reduced mass appears in a simple calculation of the [[Rydberg constant]] and Rydberg equation, but the reduced mass also appears in the [[Schrödinger equation]], and the [[Dirac equation]] for calculating atomic energy levels.

The reduced mass of the system in these equations is close to the mass of a single electron, but differs from it by a small amount about equal to the ratio of mass of the electron to the nucleus. For {{sup|1}}H, this amount is about {{sfrac|1837|1836}}, or 1.000545, and for {{sup|2}}H it is even smaller: {{sfrac|3671|3670}}, or 1.0002725. The energies of electronic spectra lines for {{sup|2}}H and {{sup|1}}H therefore differ by the ratio of these two numbers, which is 1.000272. The wavelengths of all deuterium spectroscopic lines are shorter than the corresponding lines of light hydrogen, by 0.0272%. In astronomical observation, this corresponds to a blue Doppler shift of 0.0272% of the [[speed of light]], or 81.6&nbsp;km/s.<ref>{{cite journal | vauthors = Hébrard G, Péquignot D, Vidal-Madjar A, Walsh JR, Ferlet R |date=7 February 2000 |title=Detection of deuterium Balmer lines in the Orion Nebula |journal=Astronomy and Astrophysics |volume=354 |page=L79 |arxiv=astro-ph/0002141 |bibcode=2000A&A...354L..79H}}</ref>

The differences are much more pronounced in vibrational spectroscopy such as [[infrared spectroscopy]] and [[Raman spectroscopy]],<ref>{{cite web |title=Water absorption spectrum |date= |website=[[London South Bank University]] (lsbu.ac.uk) |place=London, UK |url=http://www1.lsbu.ac.uk/water/vibrat.html |url-status=dead <!-- tested 2022-12-21 --> |archive-url=https://web.archive.org/web/20170727144128/http://www1.lsbu.ac.uk/water/vibrat.html |archive-date=27 July 2017}}</ref> and in rotational spectra such as [[microwave spectroscopy]] because the [[reduced mass]] of the deuterium is markedly higher than that of protium. In [[nuclear magnetic resonance spectroscopy]], deuterium has a very different [[nuclear magnetic resonance|NMR]] frequency (e.g. 61&nbsp;MHz when protium is at 400&nbsp;MHz) and is much less sensitive. Deuterated solvents are usually used in protium NMR to prevent the solvent from overlapping with the signal, though [[deuterium NMR]] on its own right is also possible.