The Line Spectra Of The Hydrogen Atom

Step 1: Understand spectral series
For hydrogen atom transitions, wavelength is given by: where is Rydberg constant, is final level, and is initial level.
Step 2: Shortest wavelength in Balmer series
Shortest wavelength corresponds to maximum energy transition ( to ):
Step 3: Shortest wavelength in Brackett series
For Brackett series ( ), shortest wavelength occurs when :
Step 4: Find the ratio