Balmer series | Paschen series | Lyman series

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The emission spectrum of atomic hydrogen can be considered in several pieces: the Balmer series, which lies mostly in the visible portion of the spectrum; the Paschen series, which lies in the infrared; and the Lyman series in the ultraviolet. The Balmer series can be described by a mathematical formula as described in Section 4.8.  Can the Paschen series and the Lyman series be described by a similar mathematical relationship?  Restart.

The units of wavelength on the graph are nm.

1. Verify that the mathematical formula works for the Balmer series.
2. Whereas the leading term in the Balmer formula contains the factor 1/2², the Paschen series and the Lyman series will contain a different factor, but the same form, one over an integer squared. What is the integer for the Paschen series and the integer for the Lyman series?
3. Try a different integer in the leading term and calculate the wavelengths of a few lines. Do they match any series?
4. What combinations of integers produce each series?
5. Does the same Rydberg constant work for each and every series?

Exploration written by Steve Mellema, Chuck Niederriter, Mario Belloni, and Wolfgang Christian.