A question regarding hydrogen emission and absorption spectrum

I have read in many articles as well as my textbook that when an electric discharge is passed through a sample of hydrogen gas it excites the electrons and glows emitting light.When this light is refracted through a prism we can see different wavelengths of visible light which is obtained from dexcitation of electrons from different energy levels like from n=4,n=5 etc.My question is that when an electric discharge is passed or the sample is heated shouldn't the electrons in all the hydrogen atoms excite to the same level and not to different levels and thus emit same wavelength of light?For example when a sample of hydrogen gas is put through an electric discharge since all atoms receive same energy shouldn't the electrons in all atoms excite to same energy level and dexcite from the same energy level like from n=2 to n=3 and back and not to different energy levels like one electron in one atom excites from n=2 to n=3 and the one electron in another atom excite from n=2 to n=4 shouldn't both excite to n=3?I hope you get an idea of what I am trying to say.


