Level: introductory
Reference: Johann Jacob Balmer, "Note on the Spectral Lines of Hydrogen," Annalen der Physik und Chemie 25, 80-5 (1885)
Notes: Johann Jacob Balmer (1825-1898) was looking for regularities among the wavelengths of the spectrum of hydrogen. Accounting for these regularities in the spectrum of hydrogen was an important aspect of Niels Bohr's model of the hydrogen atom, which was itself an important precursor of quantum mechanical descriptions of atomic structure.
Balmer reported observations by several researchers of ultraviolet lines in the hydrogen spectrum that matched the five predicted lines of the n=2 series quite well (i.e., the five wavelengths sought here in exercise 2)--although not quite so well as the four lines in the visible range. This series of hydrogen lines is now known as the Balmer series.
Balmer's speculation that there were other series of spectral lines for hydrogen was also correct; however, his extended formula (used here in exercise 3) did not quite predict their wavelengths correctly. As it happens, the constant is not the same for each series, but the constants for different series are simply related. Rather than
λ = h[m2/(m2 - n2)] ,the correct formula is
λ = k[m2n2/(m2 - n2)] ,The n=1 series begins with λ = 972 Å, in the ultraviolet; this series was named after its discoverer, Theodore Lyman. The n=3 series begins with 9545 Å, in the infrared; it too was named after its discoverer, Friedrich Paschen. There are other series as well. (See a 1922 paper by Frederick Brackett comparing Bohr's formula for the hydrogen spectral series with the Paschen series and with two members of a new series.)
Solutions: To download solutions, go to:
http://web.lemoyne.edu/giunta/classicalcs/balmer.doc
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