The most prominent feature of the hydrogen spectrum in the visible region is the red Balmer line, coming from the transition n = 3 to n = 2. First of all, determine the wavelength and frequency of this line according to the Bohr theory. Fine structure splits this line into several closely-spaced lines; the question is: How many, and what is their spacing? First determine how many sublevels the n = 2 level splits into, and find E¹_fs for each of these, in eV. Then do the same for n = 3. Draw an energy level diagram showing all possible transitions from n = 3 to n = 2. The energy released (in the form of a photon) is (E₃ - E₂) + ΔE, the first part being common to all of them, and ΔE (due to fine structure) varying from one transition to the next. Find ΔE (in eV) for each transition. Finally, convert to photon frequency, and determine the spacing between adjacent spectral lines (in Hz)—not the frequency interval between each line and the unperturbed line (which is, of course, unobservable), but the frequency interval between each line and the next one. Your final answer should take the form: “The red Balmer line splits into (???) lines. In order of increasing frequency, they come from the transitions (1) j = (???) to j = (???), (2) j = (???) to j = (???), …. The frequency spacing between line (1) and line (2) is (???) Hz, the spacing between line (2) and line (3) is (???) Hz, ….”