In physics and chemistry, the Lyman series is a hydrogen spectral series. When the electron in a hydrogen atom goes from n ≥ 2 to n = 1, (n is the principal quantum number, or electron shell), the electron gives off ultraviolet emission lines. The electron goes to n = 1 because it is the lowest energy level of the electron (the "groundstate"). The transitions are named in order by Greek letters. An electron that goes from n = 2 to n = 1 is called Lyman-alpha. An electron that goes from 3 to 1 is called Lyman-beta. An electron that goes from 4 to 1 is called Lyman-gamma, and so on. The series is named after its discoverer, Theodore Lyman. If there is a greater difference in principal quantum numbers, more electromagnetic radiation is emitted.

The version of the Rydberg formula that created the Lyman series was:^[1] $${\displaystyle {1 \over \lambda }=R_{\text{H}}\left(1-{\frac {1}{n^{2}}}\right)\qquad \left(R_{\text{H}}=R_{\infty }{\frac {m_{\text{p}}}{m_{\text{e}}+m_{\text{p}}}}\approx 1.0968{\times }10^{7}\,{\text{m}}^{-1}\approx {\frac {13.6\,{\text{eV}}}{hc}}\right)}$$ where n is a natural number bigger than or equal to 2 (i.e., n = 2, 3, 4, ...).

The lines in the picture are the wavelengths that correspond to n = 2 (on the right), then n = 3, which eventually goes to n → ∞ on the left. There can be an infinite number of spectral lines, but these lines are very dense when they get closer to n → ∞ (the Lyman limit).

The wavelengths in the Lyman series are all ultraviolet:

In 1914, when Niels Bohr made his Bohr model theory, he explained why hydrogen spectral lines fit Rydberg's formula. Bohr found that each electron's energy must be "quantized". This means that its energy level must be an integer: 1, 2, 3, 4, etc. The amount of energy for an electron based on its energy level follows this formula:

${\displaystyle E_{n}=-{\frac {m_{e}e^{4}}{2(4\pi \varepsilon _{0}\hbar )^{2}}}\,{\frac {1}{n^{2}}}=-{\frac {13.6\,{\text{eV}}}{n^{2}}}.}$

If an electron goes from a higher energy level (E_i) to a lower energy level (E_f), the atom emits radiation. The radiation has a wavelength of

${\displaystyle \lambda ={\frac {hc}{E_{\text{i}}-E_{\text{f}}}}.}$

In this equation, h is the Planck constant, and c is the speed of light. This equation can be simplified using units of electron-volts and angstroms:

${\displaystyle \lambda ={\frac {12398.4\,{\text{eV}}}{E_{\text{i}}-E_{\text{f}}}}}$Å.

• Bohr model