Hydrogen spectral series

The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula.

These observed spectral lines are due to the electron making transitions between two energy levels in an atom.

The spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen and calculating red shifts.

These states were visualized by the Bohr model of the hydrogen atom as being distinct orbits around the nucleus.

[3] The energy differences between levels in the Bohr model, and hence the wavelengths of emitted or absorbed photons, is given by the Rydberg formula:[4]

where The wavelength will always be positive because n′ is defined as the lower level and so is less than n. This equation is valid for all hydrogen-like species, i.e. atoms having only a single electron, and the particular case of hydrogen spectral lines is given by Z = 1.

Balmer lines are historically referred to as "H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen.

(nm) Named after the American physicist Frederick Sumner Brackett who first observed the spectral lines in 1922.

The seventh series of atomic hydrogen was first demonstrated experimentally at infrared wavelengths in 1972 by Peter Hansen and John Strong at the University of Massachusetts Amherst.

[16] The concepts of the Rydberg formula can be applied to any system with a single particle orbiting a nucleus, for example a He+ ion or a muonium exotic atom.

The equation must be modified based on the system's Bohr radius; emissions will be of a similar character but at a different range of energies.

The Pickering–Fowler series was originally attributed to an unknown form of hydrogen with half-integer transition levels by both Pickering[17][18][19] and Fowler,[20] but Bohr correctly recognised them as spectral lines arising from the He+ ion.

The deduction of the Rydberg formula was a major step in physics, but it was long before an extension to the spectra of other elements could be accomplished.