Balmer spectral series

Johann Balmer was looking for numerical relationships among the wavelengths that had been observed for lines in the spectrum of hydrogen. The four spectral lines known in the visible spectrum had wavelengths of 6562.10, 4860.74, 4340.1, and 4101.2 Å.[1] Balmer found that these four wavelengths fit a pattern that he expressed in the following formula:
λ = h[m2/(m2 - n2)] ,
where h is the same constant for all four lines and where m takes on whole-number values greater than 2 (that is, m = 3, 4, 5, and 6 respectively for the four lines in the visible spectrum).

1) Given the formula, determine the value of the constant h .

2) If the formula is valid, Balmer reasoned, then there may be additional lines in the hydrogen spectrum. Predict the wavelengths of the next five lines in this series (i.e., corresponding to the next five whole-number values of m).

3) Balmer speculated that there may be still other series of spectral lines that have wavelengths of:

λ = h[m2/(m2 - n2)] ,
where n is a different whole number for each series and m takes on values of whole numbers greater than n. Thus the series we have worked with so far is the n = 2 series with m = 3, 4, 5, ... . What is the first wavelength in the n =1 series? The n = 3 series? In what part of the electromagnetic spectrum would these lines fall?

Reference

Johann Jacob Balmer, "Note on the Spectral Lines of Hydrogen," Annalen der Physik und Chemie 25, 80-5 (1885)
[1]The units are 10-10 m, later called Angstroms, Å.
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.

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