# The 6 hydrogen spectral line series'

I noticed that the hydrogen spectral lines are grouped into 6 series and given a value for n. I also noticed that each series was named after its discoverer but "coincidentally?" falls into a specific region of the EM spectrum so the Lyman series (n=1) of lines are all in the UV region, the Balmer series (n=2) in the visible region, the Paschen series (n=3) the IR region etc. Firstly is this "n" the principle quantum number? If so what have these series' got to do with the different energy shells of the Bohr model? For example what has the balmer series got to do with the 2nd energy shell? Finally what is it about this correlation that causes the lines of each series to appear where they do. For example why do the lines all appear in the UV region when n=1 but lie in the visible region when n=2?

## Answers and Replies

jtbell
Mentor
See the Rydberg formula for hydrogen. $n_2$ is the principal quantum number ("energy shell number") of the atom before a transition. $n_1$ is the principal quantum number of the atom after a transition.

So the n=1 series is all the spectral lines emitted by electrons as they fall back to the 1st energy shell. Why do they all emit UV radiation? If the energy emitted is the energy difference between the 2 energy levels then it makes sense that Lyman lines are higher in energy than Balmer lines but the photon emitted by an electron dropping from n=6 back to n=2 would he higher in energy than say n=2 back to n=1 wouldn't it?

Last edited:
phyzguy
Science Advisor
but the photon emitted by an electron dropping from n=6 back to n=2 would he higher in energy than say n=2 back to n=1 wouldn't it?

No, it wouldn't, because the levels aren't equally spaced. Try plugging in the numbers. The energy of an n=2 to n=1 photon is 13.6eV(1/1-1/4) = 10.2eV. The energy of an n=6 to n=2 photon is 13.6eV(1/4-1/36) = 3.02eV.

Ah right, that explains it. Thanks a lot!