This is more of an understanding issue than a homework problem, but if I don't understand, I can't prepare for homework. With regard to energy level transitions, the text states almost as an afterthought that "Transitions between the same energy levels always produce the same frequency emission. The frequency is the cause of visible color." And, that's ALL it states about that issue...end of story.
First, I never considered same energy-level transitions. I understand transitions above then back to ground state. In transitions to the same energy level, does the electron gain only enough energy to jump to a degenerate orbital? Are they using the term "color" loosely? If I use the same energy level in n and n', Rydberg gives me zilch when calculating wavelength. If a photon is released, there must be a wavelength. How is it determined and why would the frequency emission be the same in every single case of same energy level transitions? I feel like I've totally missed the boat after those two "oh-by-the-way" type sentences.
1/l = R [(1/n'^2)-(1/n^2)] although I don't think this equation will apply here.
The Attempt at a Solution
I don't understand the text itself, so I don't have an explanation. I'm looking for the explanation as to how a same energy level transition occurs and how a frequency would be generated. I'm assuming the e- absorbs a little energy, but not enough to throw it into a higher E level, and when that energy is released, a photon is emitted, but why are all those absorbed energies assumed to be the same in order for them to generate the exact same frequency in every case as the text states? How would one calculate a wavelength?
Thanks in advance for your assistance.