Balmer series wavelength prediction

The atomic emission spectrum of hydrogen is composed of many lines but these fall into separate sets or series. The first series to be discovered, not surprisingly, were those lines in the visible part of the spectrum. In 1885, a Swiss schoolmaster, Johann Balmer, noticed that the wavelengths, A, of the lines in this series could be predicted using a mathematical formula. He did not see why he just saw the relationship. This was the first vital step. 

Aware of only these four hues, Balmer calculated 1 for a fifth hue lyn = 7). A hue with a wavelength very close to the predicted value was observed experimentally. Balmer suggested that his formula might also predict wavelengths of other series of spectral fines by using integer values for n other than 2 and rw n L 1. Other series of hydrogen lines were not known then, but were subsequently discovered (the Lyman, Paschen, Brackett, and Pfund series of fines). 

Predict the wavelengths of the next two lines in this series and the wavelength of the series limit. (Balmer was a Swiss mathematician who, in 1885, came up with an empirical formula that fitted lines of the hydrogen spectrum.)... 

In this relationship, m is an integer greater than 2, with each value of m representing a different spectral line. Balmer was able to predict the wavelength of some spectral lines that were in the near ultraviolet range. The success of Balmer s equation was strengthened when other spectral series of emission lines were discovered in the ultraviolet (Lyman series) and in the infrared (Paschen series). The lines in their series could be determined by modified Balmer equations ... 

---