Physlet Illustration: The Spectrum of Atomic Hydrogen
Balmer Paschen Lyman

 

 
The 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.  Can the Paschen and Lyman series by described by a similar mathematical relationship?  

Hints:

  1. Can you verify that the mathematical formula works for the Balmer series?  
  2. Whereas the leading term in the Balmer formula contains 22, the Paschen and Lyman series will contain a different integer squared.  What might the integer be?
  3. Try a different integer in the leading term and calculate the wavelengths of a few lines.  Do they match any series?
  4. Does the same Rydberg constant work for all of the series?
  5. What combinations of integers produce each of the series? 

Reference

See Walker, Sections 31-2

Illustration written by Modified by Chuck Niederriter