Bohr Hydrogen Spectrum

An electron bound to a proton cannot sit at just any energy. It is restricted to a ladder of levels, E_n = -13.6 eV over n squared, crowding together as they climb toward zero. When the electron drops from a higher rung to a lower one it sheds the exact energy difference as a single photon, and that fixed energy is a fixed colour. So hydrogen does not glow across a smooth rainbow; it emits only a sparse, exact set of lines. Drops landing on n = 1 make the ultraviolet Lyman series, drops landing on n = 2 make the Balmer series whose first few lines fall in the visible (the red H-alpha at 656 nm is the colour of glowing nebulae), and higher landings give infrared series. Each series fans toward a limit and stops. This barcode is how we read the universe: the same lines, shifted by a star's motion, tell us what it is made of and how fast it moves. The scene shows the energy ladder and a falling electron; the diagnostic is the spectrum it writes.

Figure 1. Bohr model of the hydrogen spectrum. Top: the energy levels E_n = -13.6 eV / n squared, with an electron transition emitting a photon. Bottom: the emission spectrum, each transition a coloured line at its wavelength (true colours in the visible band), grouped into the Lyman, Balmer, Paschen and higher series. Method: E_n = -E_R/n squared; 1/lambda = R_H (1/n_low squared - 1/n_high squared).

seriesBalmer

from n3

WHAT TO TRY

Keep Balmer and drop from n = 3: the electron emits the red H-alpha line at 656 nm, the glow of hydrogen nebulae.
Raise the upper level and watch the line shift toward the blue and crowd toward the series limit.
Switch to Lyman: every line jumps into the ultraviolet; switch to Paschen and they go infrared.
Notice the levels crowd toward zero, so each series has a sharp short-wavelength limit it never passes.