[mana]

hi all
as we know the excited electron by the cathodic ray will emit an X-ray in its return to the ground state, and line spectra will be recorded as a result. my question is what is the relationship between the number of lines in line spectra and the possibilities of electron transitions? for example in the picture below, I expect 6 lines in the spectra (6 transitions to n=2 in the visible zone) but there are 4 lines how it can be explained?
thanks for your help in advance

[Borek]

the excited electron by the cathodic ray will emit an X-ray in its return to the ground state

X-ray?

I expect 6 lines in the spectra (6 transitions to n=2 in the visible zone)

Why do you expect them to be in the visible light? You should calculate energies for all possible transitions, and count those in the visible range only.

But, broadly speaking, this is much more complicated. There are many reasons why some lines can't be detected - in general not all transitions are equally probable (so some are more/less intense than others), not all energy levels are equally occupied (which again leads to differing intensity, with some so dark they lie below detection limits), lines are never infinitesimally narrow, they will overlap, making their separation impossible - and so on.

[mana]

the excited electron by the cathodic ray will emit an X-ray in its return to the ground state

X-ray?

yes

[mana]

thank you dear borek, I get the answer

[Borek]

Formatting was broken, I hope I corrected it right:

the excited electron by the cathodic ray will emit an X-ray in its return to the ground state

X-ray?

yes

Well, if the excited electron emits X-Ray it by definition doesn't emit in visible light, something is wrong here.

Are you sure you are not mistaking fast electrons that "do the exciting" for the excited electrons in hydrogen atoms?