Light as Information

Section 6 of 9

Atoms and Spectral Lines

Part 6: Atoms and Spectral Lines

The Sun’s spectrum isn’t a smooth rainbow — it’s crossed by hundreds of dark absorption lines. They aren’t imperfections; they’re information. The key idea: atoms have quantized energy levels.

The Bohr Model

Modern quantum mechanics is deeper, but the Bohr model gets the essential story right and gives correct energies for hydrogen. The electron can only occupy discrete levels labeled by an integer $n = 1, 2, 3, \dots$

Bohr model

An early model of the atom in which an electron occupies discrete, quantized energy levels labeled by an integer $n$ . It correctly predicts hydrogen’s energy levels and spectral lines, and supplies the intuition behind quantum atomic structure.

For hydrogen, the energy of level $n$ is:

The ground state ( $n=1$ ) is the most tightly bound; higher levels have energies closer to zero (less bound, easier to ionize).

Photon Absorption and Emission

When an electron changes levels, the atom absorbs or emits a photon whose energy matches the difference:

$\Delta E = E_{\text{upper}} - E_{\text{lower}} = h\nu = \frac{hc}{\lambda}.$

An absorption line appears when photons of a particular energy are removed because electrons jump up; an emission line appears when a thin gas produces photons as electrons fall down.

Left: Bohr model of hydrogen with electron falling between levels. Right top: energy level diagram showing electron emitting photons while dropping down. Right bottom: emission spectrum with bright lines at specific wavelengths. — Figure 12Hydrogen emits specific wavelengths because electrons fall DOWN between energy levels. Each bright line = one electron transition. The Balmer series (visible) comes from transitions to level 2.JWST/STScI

Kirchhoff’s Laws: Three Types of Spectra

Kirchhoff’s laws identify three basic spectrum shapes, each from a different physical situation — this is how we know what stars are made of without sampling them.

Kirchhoff's laws

Three rules linking a spectrum’s appearance to its source: (1) a hot dense object gives a continuous spectrum; (2) a hot thin gas gives an emission-line spectrum; (3) cool gas in front of a hot continuous source gives an absorption-line spectrum.

A continuous spectrum comes from hot, dense matter (a blackbody-like source). An absorption spectrum arises when cool gas sits in front of a hot continuous source. An emission spectrum comes from hot, thin gas with no bright background. The remarkable thing: the same atoms produce both absorption and emission — what changes is the density/temperature structure and whether there’s a bright continuum behind the gas.

Continuous spectrum

A smooth spectrum spanning all wavelengths, with no lines — emitted by a hot, dense (blackbody-like) source such as a stellar interior.

Absorption spectrum

A continuous spectrum crossed by dark lines, produced when cooler gas in front of a hot continuous source removes photons at its characteristic wavelengths. Stellar spectra are absorption spectra.

Emission spectrum

Bright lines on a dark background, produced by a hot, thin gas with no bright continuum behind it — for example, an emission nebula.

Spectral lines reveal more than composition: which transitions are populated gives temperature; Doppler shifts give velocity; line widths give density/pressure — all developed in Module 2.