Editing Rydberg constant (section)

== Precision measurement ==
{{See also|Precision tests of QED}}
The Rydberg constant was one of the most precisely determined physical constants, with a relative standard uncertainty of {{physconst|Rinf|runc=yes|after=.}} This precision constrains the values of the other physical constants that define it.<ref name="codata">P.J. Mohr, B.N. Taylor, and D.B. Newell (2015), "The 2014 CODATA Recommended Values of the Fundamental Physical Constants" (Web Version 7.0). This database was developed by J. Baker, M. Douma, and [[Svetlana Kotochigova|S. Kotochigova]]. Available: http://physics.nist.gov/constants. National Institute of Standards and Technology, Gaithersburg, MD 20899. [http://physics.nist.gov/cgi-bin/cuu/Value?ryd Link to R<sub>∞</sub>], [http://physics.nist.gov/cgi-bin/cuu/Value?rydhcev Link to hcR<sub>∞</sub>].  Published in {{cite journal|doi=10.1103/RevModPhys.84.1527|postscript=""|title=CODATA recommended values of the fundamental physical constants: 2010|year=2012|last1=Mohr|first1=Peter J.|last2=Taylor|first2=Barry N.|last3=Newell|first3=David B.|journal=Reviews of Modern Physics|volume=84|issue=4|pages=1527–1605|arxiv = 1203.5425 |bibcode = 2012RvMP...84.1527M |s2cid=103378639}} and {{Cite journal|doi=10.1063/1.4724320|postscript=""|title=CODATA Recommended Values of the Fundamental Physical Constants: 2010|year=2012|last1=Mohr|first1=Peter J.|last2=Taylor|first2=Barry N.|last3=Newell|first3=David B.|journal=Journal of Physical and Chemical Reference Data|volume=41|issue=4|pages=043109|bibcode = 2012JPCRD..41d3109M |arxiv=1507.07956}}.</ref>

Since the Bohr model is not perfectly accurate, due to [[fine structure]], [[hyperfine splitting]], and other such effects, the Rydberg constant <math>R_{\infty}</math> cannot be ''directly'' measured at very high accuracy from the [[atomic spectral line|atomic transition frequencies]] of hydrogen alone. Instead, the Rydberg constant is inferred from measurements of atomic transition frequencies in three different atoms ([[hydrogen]], [[deuterium]], and [[antiprotonic helium]]). Detailed theoretical calculations in the framework of [[quantum electrodynamics]] are used to account for the effects of finite nuclear mass, fine structure, hyperfine splitting, and so on. Finally, the value of <math>R_{\infty}</math> is determined from the [[best fit]] of the measurements to the theory.<ref name=codata2006paper>{{cite journal |doi=10.1103/RevModPhys.80.633  |title=CODATA recommended values of the fundamental physical constants: 2006 |journal=Reviews of Modern Physics |volume=80 |pages=633–730 |year=2008|bibcode=2008RvMP...80..633M |issue=2|arxiv = 0801.0028 |last2=Taylor |last3=Newell |last1=Mohr |first1=Peter J. |first2=Barry N. |first3=David B. }}</ref>