Atomic spectra and the hydrogen spectrum

Pass white light through a prism and you get a continuous spectrum: all the colours, merging into one another, like a rainbow.

Atoms behave differently. When the atoms of a gas are excited (by heat or electricity), they give out light of only certain wavelengths, seen as bright lines on a dark background: a line (emission) spectrum. If white light is passed through the cool gas instead, the same wavelengths are absorbed, leaving dark lines on a bright background: an absorption spectrum, the negative of the emission spectrum.

Every element has its own line spectrum, as unique as a fingerprint. Scientists use it to identify elements, even in distant stars; some elements, such as helium, were discovered this way.

Hydrogen has the simplest spectrum. Rydberg found that the wavenumbers of all its lines fit one formula:

ν̄ = 109 677 (1/n₁² – 1/n₂²) cm⁻¹, where n₁ = 1, 2, 3 … and n₂ is greater than n₁.

The lines fall into series, each named after its discoverer and fixed by the value of n₁:

An electron in a high level can fall in steps by many routes. From level n, the number of different lines possible is n(n – 1)/2. From n = 5 down to n = 1, for example: 5 × 4 ÷ 2 = 10 lines.