Illustrated Physics
physics, drawn
Concept

Spectral line — where it appears

A narrow range of wavelengths at which an atom or molecule emits or absorbs, fixed by the energy difference between two of its levels. Its position identifies the substance, and its splitting, width and shift measure fields, temperatures and motions.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

One level, split by the speed of the electron in it. Hydrogen's n = 2 level on the left at the scale of the whole spectrum, and the same level on the right at a scale ten thousand times finer. The gross structure puts it 3.4014 electronvolts below the ionisation limit; the relativistic and spin–orbit corrections then split it into a lower pair, j = ½, and an upper, j = 3/2, separated by 45.3 microelectronvolts. That gap is 1.331e-5 of the level's own binding energy, which is exactly α²/4 — so the size of the splitting is a measurement of how fast the electron is going, α being its speed in units of c on the innermost orbit. The same physics in sodium is larger by four orders of magnitude: its two D lines at 588.995 and 589.5924 nanometres differ by 2.133 millielectronvolts, which is 1.01e-3 of the transition energy, because the outer electron of sodium penetrates to where the nuclear charge is far from screened and the correction goes as the fourth power of the charge it sees.

The line that is really two

Sodium's yellow line is two lines six-tenths of a nanometre apart, and the gap is not a property of the light. It is a splitting of the atom's own level, caused by the electron's magnetic moment sitting in the field it sees because it is moving — and its size, relative to the level it splits, is exactly α²/4.

quantum · Atomic spectra The levels that refuse to cross. The six energies of sodium 3p against an applied field from zero to 4 crossover fields, 147 T, from diagonalising spin–orbit coupling and the field together. At zero field there are two levels, 515.5 GHz apart. The two states with the largest |mⱼ| are straight lines at every field, because nothing else shares their mⱼ. The other four bend. The two states with mⱼ = −½ approach within 486.0 GHz near 12.3 T and then separate again — √2 ζ exactly, since the coupling between them sets how close they may come — while the mⱼ = −3/2 state falls straight through the lower mⱼ = +½ state at 16.6 T as if it were not there. States that the field cannot mix cross freely; states it can mix exchange character instead, and that exchange is the passage from one pattern to the other.

The field an atom calls strong

A magnetic field splits sodium's two yellow lines into ten, at spacings set by Landé's factors — until the field grows past the one the electron already feels from its own motion, when the ten reorganise into the three a theory without spin predicts. Nothing about the magnet decides which pattern appears. The atom does: the same 45 tesla is a strong field for hydrogen, a middling one for sodium and a weak one for caesium.

quantum · Atomic spectra

Named alongside it

The objects these essays reach for when they reach for this one.

Angular momentumAtomic spectraDegeneracyEnergy levelsFine structure constantMagnetic momentSelection rulesSpinRelativistic correctionResolving powerScreeningSymmetry

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