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Home » Chemistry Homework Help » Physical Chemistry » Hydrogen Atom Spectra
Hydrogen Atom Spectra
The analysis of hydrogen atom spectra illustrates how atomic spectra yield information about the energies of atoms.

The radiation emitted by high energy, or “excited” atoms produces line spectra. An example is provided by the schematic, composite line spectrum of hydrogen of hydrogen atoms shown in as that  illustrates, only a particular wavelength, or frequencies, of radiation are emitted by the atoms.

When atomic line spectra were first studied, in the late 1800s, many unsuccessful attempts were made to explain the observed spectral lines of the atoms as harmonic or overtones of some set of fundamental frequencies. In 1885 J. J Balmer showed that the frequencies of some of the observed spectral lines of hydrogen atoms, now known as the Balmer series, could be expressed by a completely empirical relation. This empirical approach was soon extended, and J. R. Rydberg showed that the frequencies of all the hydrogen atom spectral lines were generated by the expression:

V = R (1/n22 – 1/n12)   n2 = 1, 2, 3 …

                                        n1 = 2, 3, 4 ….


When the Rydberg constant R in this Rydberg formula is given the value 3.2880 × 1015 s-1, the frequencies of all the lines of hydrogen atom spectra are generated by the various combinations of n1 and n2 values.

Wave numbers: convenient numerical values related to the frequencies of atomic spectral lines are obtained by introducing the wave number v, defined by v = 1/γ, wave numbers, which are less than those of frequencies by a factor equal to the speed of light. Wave numbers, which are reciprocals of wavelength, are traditionally expressed with cm-1 units.

The value of the Rydberg constant needed to produce the wave number values for the hydrogen atom spectral lines is:

R = 3.2880 × 1015 s-1/2.9979 × 1010 cm s-1 = 109,677 cm-1

The Rydberg formula suggests that the observed spectral lines can be grouped into series, the lines of each series being generated when a particular value of n2 is used in the Rydberg formula. These series were, in fact, recognized in the line spectra, and they are identified by the names of their discoverers.

The Rydberg formula suggests that the observed spectral lines can be grouped into series, the lines of each series being generated when a particular value of n2 is used in Rydberg formula. These series were, in fact, recognized in the line spectra, and they are identified by the names of their discoverers.

Hydrogen-Atom spectra series and Rydberg integers:

Series n2 n1 Spectral region
Lyman 1 2, 3, 4…. Ultraviolet
Balmer 2 3, 4, 5….. Visible
Paschen 3 4, 5, 6….. Infrared
Brackett 4 5, 6, 7…. Infrared
Pfund 5 6, 7, 8….  Infrared

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