氢原子光谱Hydrogen spectral series

巴耳末系的四条可见谱线为 656.3 nm（红，Hα）、486.1 nm（蓝绿，Hβ）、434.0 nm（蓝紫，Hγ）和 410.2 nm（紫，Hδ），向短波方向逐渐密集，收敛于系限 364.6 nm。玻尔模型把谱线解释为电子从高能级 n₂ 跃迁到低能级 n₁ 时放出光子，能量 hν = Eₙ₂ − Eₙ₁ = 13.6 eV × (1/n₁² − 1/n₂²)。谱线的分立性直接证明了原子能量的量子化。

The four visible Balmer lines are at 656.3 nm (red, Hα), 486.1 nm (blue-green, Hβ), 434.0 nm (violet, Hγ) and 410.2 nm (violet, Hδ); they crowd together toward shorter wavelength and converge on the series limit at 364.6 nm. The Bohr model explains each line as a photon emitted when the electron falls from level n₂ to n₁, with hν = Eₙ₂ − Eₙ₁ = 13.6 eV × (1/n₁² − 1/n₂²). The discreteness of the lines directly proves that atomic energies are quantised.

1885 年瑞士中学教师巴耳末找到可见谱线波长的经验公式 λ = B·n²/(n² − 4)。1888 年里德伯推广为普遍公式。1906 年莱曼发现紫外系，1908 年帕邢发现红外系，之后又发现布拉开系（1922）、普丰德系（1924）和汉弗莱斯系（1953）。1913 年玻尔的原子模型首次从理论上导出这些规律。精细结构和兰姆位移（1947）的发现推动了相对论量子力学和量子电动力学的发展。

In 1885 the Swiss schoolteacher Johann Balmer found an empirical formula for the visible lines, λ = B·n²/(n² − 4), which Rydberg generalised in 1888. Lyman found the ultraviolet series in 1906 and Paschen the infrared series in 1908, followed by the Brackett (1922), Pfund (1924) and Humphreys (1953) series. Bohr's 1913 atomic model first derived these regularities theoretically. Fine structure and the Lamb shift (1947) drove the development of relativistic quantum mechanics and quantum electrodynamics.

天文学中利用 Hα 线观测星云和太阳色球；通过谱线红移测定星系退行速度。氢的 21 cm 超精细跃迁谱线用于绘制银河系的结构。氢光谱的精密测量是检验量子电动力学和测定里德伯常数、质子半径的重要手段。

Astronomers use the Hα line to observe nebulae and the solar chromosphere, and the redshift of hydrogen lines to measure the recession of galaxies. The 21 cm hyperfine line of hydrogen maps the structure of the Milky Way. Precision hydrogen spectroscopy tests quantum electrodynamics and determines the Rydberg constant and the proton radius.