Rydberg-Ritz combination principle

The Rydberg-Ritz combination principle is an empirical relationship proposed by Walter Ritz in 1908 to explain the relationship among spectral lines of the hydrogen atom. The principle states that the spectral lines of the hydrogen atom include frequencies that are either the sum or the difference of the frequencies of two other lines. This principle is obvious to us, because we now know that spectra arise from transitions between energy levels. 

The frequencies of the first ten lines of an emission spectrum of hydrogen are given in the table at the bottom of this page. In this problem, use ideas from this chapter to identify the transitions involved, and apply the Rydberg-Ritz combination principle to calculate the frequencies of other lines in the spectrum of hydrogen. 

In both the Balmer and the Rydberg formulae the wave-number of a spectral line is given by the difference of two quantities. In 1908 Ritz showed experimentally that in any spectrum it was possible to set up tables of quantities called terms, having dimensions of cm, such that the wave-numbers of the observed spectral lines could be written as the difference of two terms. This is known as the Ritz combination principle. In hydrogen, new spectral series were predicted with lines given by... 

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