Line spectra of hydrogen

A transition from a higher level ni to a lower level nf (nf < ni) sends out a photon of frequency νif with hνif = Eni − Enf (Eq. 12.11).

Both ni and nf are whole numbers, so only certain energy differences, and so only certain discrete frequencies, are possible: this is the line spectrum.

Emission lines come from electrons dropping from higher to lower states. Absorption happens when an atom takes in a photon whose energy exactly matches the gap to a higher state.

Light with a continuous range of frequencies passed through a rarefied gas therefore comes out with dark absorption lines at the frequencies the atoms absorbed.

For hydrogen, hν = 13.6 eV (1/nf² − 1/ni²). Using hc ≈ 1240 eV nm: 2 → 1 gives 10.2 eV (about 122 nm, ultraviolet); 3 → 1 gives 12.09 eV (about 103 nm); 3 → 2 gives 1.89 eV (about 656 nm, red).

Bohr's explanation of the hydrogen spectrum was a major achievement that drove the development of quantum theory, and he received the Nobel Prize in Physics in 1922.