# 里德伯常量

${\displaystyle R_{\infty }=1.0973731568508(65)\times 10^{7}\,\mathrm {m} ^{-1}}$[1]

${\displaystyle {\frac {1}{\lambda }}=R({\frac {1}{n^{2}}}-{\frac {1}{n'^{2}}})\qquad n=1,2,3\cdots \quad n'=n+1,n+2,n+3\cdots }$

1913年丹麦物理学家尼尔斯·波尔创立的波尔模型给出了里德伯常量的表达式：

${\displaystyle R={\frac {2\pi ^{2}m_{e}e^{4}}{(4\pi \varepsilon _{0})^{2}ch^{3}}}}$

${\displaystyle m_{e}}$电子质量
${\displaystyle e}$电荷
${\displaystyle \varepsilon _{0}}$真空电容率
${\displaystyle c}$光速
${\displaystyle h}$普朗克常数

${\displaystyle R=109737.315\mathrm {cm^{-1}} }$

${\displaystyle R=109677.58\mathrm {cm^{-1}} }$

${\displaystyle \mu ={\frac {m_{e}M}{m_{e}+M}}}$

${\displaystyle R_{\infty }={\frac {2\pi ^{2}m_{e}e^{4}}{(4\pi \varepsilon _{0})^{2}ch^{3}}}={\frac {\alpha ^{2}m_{e}c}{4\pi \hbar }}={\frac {\alpha ^{2}}{2\lambda _{e}}}}$

${\displaystyle \alpha }$精细结构常数
${\displaystyle \lambda _{e}}$是电子的康普顿波长

${\displaystyle R_{A}={\frac {R_{\infty }}{1+{\frac {m_{e}}{M}}}}}$

1H：109 677.58 cm-1
2D：109 707.42 cm-1
3T：109 717.35 cm-1
4He+：438710.32 cm-1
7Li2+：987098.22 cm-1
8Be3+：1754841.28 cm-1

## 里德伯能量

${\displaystyle 1\ {\text{Ry}}:=hcR_{\infty }=13.605693009(84)\,{\text{eV}}.}$[2]

## 參考資料

1. ^ CODATA Value: Rydberg constant. physics.nist.gov. [2016-12-09]. （原始内容存档于2021-05-06）.
2. ^ P.J. Mohr, B.N. Taylor, and D.B. Newell (2011), "The 2010 CODATA Recommended Values of the Fundamental Physical Constants" (Web Version 6.0). This database was developed by J. Baker, M. Douma, and S. Kotochigova. Available: http://physics.nist.gov/constants页面存档备份，存于互联网档案馆）. National Institute of Standards and Technology, Gaithersburg, MD 20899. Link to R页面存档备份，存于互联网档案馆）, Link to hcR页面存档备份，存于互联网档案馆