Editing Rydberg constant (section)

== Value ==
=== Rydberg constant === 
The [[CODATA]] value is
: <math> R_\infty = \frac{m_\text{e} e^4}{8 \varepsilon_{0}^{2} h^3 c} = </math> {{physconst|Rinf|after=,}}
where
* <math>m_\text{e}</math> is the [[rest mass]] of the [[electron]] (i.e. the [[electron mass]]),
* <math>e</math> is the [[elementary charge]], 
* <math>\varepsilon_0</math> is the [[permittivity of free space]], 
* <math>h</math> is the [[Planck constant]], and 
* <math>c</math> is the [[speed of light]] in vacuum.

The symbol <math>\infty</math> means that the nucleus is assumed to be infinitely heavy, an improvement of the value can be made using the [[reduced mass]] of the atom:
: <math>\mu = \frac{ 1 }{ \frac{1}{m_\text{e}} + \frac{1}{M} }</math>
with <math>M</math> the mass of the nucleus. The corrected Rydberg constant is:
: <math>R_\text{M} = \frac{ \mu }{ m_\text{e} }R_\infty </math>
that for hydrogen, where <math>M</math> is the mass <math>m_\text{p}</math> of the [[proton]], becomes:
: <math>R_\text{H} = \frac{ m_\text{p} }{ m_\text{e}+m_\text{p} }R_\infty  \approx 1.09678 \times 10^7 \text{ m}^{-1} ,</math>

Since the Rydberg constant is related to the spectrum lines of the atom, this correction leads to an [[isotopic shift]] between different isotopes. For example, deuterium, an isotope of hydrogen with a nucleus formed by a proton and a [[neutron]] (<math>M = m_\text{p} + m_\text{n}\approx 2m_\text{p}</math>), was discovered thanks to its slightly shifted spectrum.<ref>''Quantum Mechanics'' (2nd Edition), B.H. Bransden, [[Charles J. Joachain|C.J. Joachain]], Prentice Hall publishers, 2000, {{ISBN|0-582-35691-1}}</ref>

=== Rydberg unit of energy ===
The Rydberg unit of energy is
: <math>1 \ \text{Ry} ~~ \equiv h c\, R_\infty = \alpha^2 m_\text{e} c^2 /2</math>
::: = {{physconst|Rinfhc}}
::: = {{physconst|Rinfhc_eV}}

=== Rydberg frequency ===
: <math>c R_\infty</math> = {{physconst|Rinfc|after=.}}

=== Rydberg wavelength ===
: <math>\frac 1 {R_\infty} = 9.112\;670\;505\;826(10) \times 10^{-8}\ \text{m}</math>.

The corresponding [[angular wavelength]] is
: <math>\frac 1 {2\pi R_\infty} = 1.450\;326\;555\;77(16) \times 10^{-8}\ \text{m}</math>.