Quantised. The energy levels in an atom are quantised: the electron can only exist at specific, discrete, fixed energy levels. The electron cannot sit between two levels.

A bound system. The electron is bound to the atom. 0 eV is the ionisation level, where the electron is free. A bound electron has less energy than a free electron, so every bound level is negative. The ground state is −13.6 eV, so 13.6 eV must be supplied to free the electron from the ground state. This is the ionisation energy.

Excitation is when an electron absorbs energy and moves from a lower to a higher energy level. De-excitation is when an electron releases a photon and moves from a higher to a lower energy level and becomes more stable.

Photon or electron. A photon gives all of its energy or none. The photon is absorbed if its energy exactly equals the difference between two levels, or if the photon has enough energy to ionise the atom (13.6 eV or more from the ground state). In ionisation, any energy above the ionisation energy becomes the kinetic energy of the freed electron. An incoming electron can give some, all or none of its kinetic energy, and keeps the rest. If no energy is transferred, the collision is elastic: the incoming electron keeps all of its kinetic energy. If the incoming electron gives energy to excite or ionise the atom, the collision is inelastic: the incoming electron loses that energy.

Absorption and emission. Both kinds of spectral line come from the same energy levels. The dark absorption lines are at the same wavelengths as the bright emission lines because the same gaps between levels are involved. Cool hydrogen with every electron in the ground state absorbs only ultraviolet. The visible absorption lines come from atoms with an electron already in n = 2, as in the outer layers of a star.

The numbers. The calculations use the level energies shown and h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m/s, e = 1.60 × 10⁻¹⁹ C, so the wavelengths match a calculator. The measured visible lines are 656, 486, 434 and 410 nm. Real hydrogen has more levels between n = 6 and 0 eV; this model stops at n = 6.

The drawings. The level diagram is not to scale: the levels are spread out so they can be read. On the spectra, the visible region is to scale; the ultraviolet and infrared margins are squashed so their lines fit on the bar.