Spectral lines of hydrogen

Heat hydrogen gas or pass a spark through it, and it gives out light of only certain wavelengths: a line spectrum. Each element has its own pattern, like a fingerprint.

Bohr's explanation: an electron that jumps down from a higher level E_i to a lower level E_f emits one photon carrying exactly the difference:

hν = E_i – E_f

Since only certain levels exist, only certain photon energies, and so certain wavelengths, can appear.

Example: from n = 2 to n = 1. ΔE = –3.4 – (–13.6) = 10.2 eV. λ = 1240/10.2 ≈ 122 nm, in the ultraviolet.

The lines fall into series, grouped by the level the electron lands on:

All of them fit one formula: 1/λ = R (1/n_f² – 1/n_i²), with the Rydberg constant R ≈ 1.097 × 10⁷ m⁻¹.

Absorption is the same in reverse: cold hydrogen absorbs only photons whose energy exactly matches a jump upwards. White light passed through it shows dark lines at the same wavelengths as the bright emission lines.

An atom raised to level n can fall back in many steps. The number of possible lines from level n is n(n – 1)/2: from n = 4, there are 6 lines.

Electron beams excite atoms too, but an electron with energy K can only lift the atom to levels within K of the ground state.