里德伯公式Rydberg formula

该公式本是经验规律，后由玻尔模型从理论上导出：R∞ = m_e·e⁴/(8ε₀²h³c) = 10 973 731.568 m⁻¹，是目前测得最精确的物理常数之一（相对不确定度约 10⁻¹²）。考虑原子核的有限质量，氢的里德伯常数 R_H = R∞/(1 + m_e/m_p) ≈ 1.096 78 × 10⁷ m⁻¹。用里德伯能量表示，氢原子电离能为 1 Ry = 13.606 eV。

An empirical rule at first, the formula was derived by the Bohr model: R∞ = m_e·e⁴/(8ε₀²h³c) = 10,973,731.568 m⁻¹, one of the most precisely measured physical constants (relative uncertainty about 10⁻¹²). Allowing for the finite nuclear mass, hydrogen's value is R_H = R∞/(1 + m_e/m_p) ≈ 1.096 78 × 10⁷ m⁻¹. Expressed as energy, hydrogen's ionisation energy is 1 Ry = 13.606 eV.

1888 年瑞典物理学家约翰内斯·里德伯在研究碱金属光谱时，把巴耳末公式改写为波数形式，发现各种元素的谱线都可写成两个“光谱项”之差，常数 R 对不同元素几乎相同。1908 年里兹提出组合原理，任意两个光谱项之差都可能是一条谱线。1913 年玻尔模型揭示光谱项就是原子能级除以 hc。

In 1888 the Swedish physicist Johannes Rydberg, studying alkali-metal spectra, rewrote Balmer's formula in wavenumbers and found that every element's lines could be written as differences of two 'terms', with a constant R nearly the same for all. In 1908 Ritz stated the combination principle, that the difference of any two terms may be a line. Bohr's 1913 model showed the terms are atomic energy levels divided by hc.

对类氢离子（He⁺、Li²⁺）乘以 Z²；对碱金属原子引入量子亏损 δ，写成 1/(n − δ)²。主量子数很大（n > 30）的“里德伯原子”半径可达微米级，对电场极其敏感，被用于量子计算和精密测量。里德伯常数的精密测定也用来确定质子电荷半径。

For hydrogen-like ions (He⁺, Li²⁺) multiply by Z²; for alkali atoms introduce a quantum defect δ and write 1/(n − δ)². 'Rydberg atoms' with very large principal quantum numbers (n > 30) can be micrometres across and extremely sensitive to electric fields, and are used in quantum computing and precision measurement. Precise measurement of the Rydberg constant also helps fix the proton's charge radius.