## Section 4.9: Exploring the Emission Spectrum of Atomic Hydrogen

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.

- Verify that the mathematical formula works for the Balmer series.
- Whereas the leading term in the Balmer formula contains the factor 1/2
^{2}, 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? - Try a different integer in the leading term and calculate the wavelengths of a few lines. Do they match any series?
- What combinations of integers produce each series?
- Does the same Rydberg constant work for each and every series?

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

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