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 5 essays across 2 fields — 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 The redshift of a white dwarf weighs it. The gravitational redshift at the surface of a cold white dwarf, expressed as the velocity that would give the same Doppler shift, against the star's mass; computed from the radius each mass is forced to have. The Sun's surface redshift is 636 m/s. A white dwarf of 0.6 solar masses shifts its light by 30.1 km/s, one of 1.0 by 77.6, of 1.2 by 128 and of 1.35 by 223. Because the radius is not free, the curve is single-valued and steepening: a measured shift returns one mass. The cold model puts Sirius B, at 1.018 solar masses, at 80.8 km/s; its measured mass and radius together give 80.0.

The redshift that weighs a dead star

Light leaving the surface of an ordinary star is reddened by gravity, but the shift alone says little, because a star's radius is free and the shift depends on mass over radius. A white dwarf has no free radius. Degenerate electrons fix its size from its mass, so one measured line shift returns one mass — and the gauge grows sharper the closer the star is to collapse. The first measurement of it, in 1925, was hailed as a confirmation of general relativity and was wrong by a factor of four, in agreement with a forecast that was wrong by the same factor.

astrophysics · Gravitational redshift The hyperfine structure, read off a room-temperature cell. The difference between the probe's absorption with the pump off and on, which removes the Doppler hump and leaves only the Doppler-free features, against detuning. The three transitions, labelled by the excited level F′, sit at −423.6, −266.65 and 0 MHz, and the three crossovers midway between them at −345.1, −211.8, −133.3 MHz. In this model, which empties the ground level only by exciting it, the crossover between F′ = 2 and 3 is the second strongest feature and the weak transitions to F′ = 1 and 2 are small. In real rubidium spectra the crossovers are often the strongest of all, because excited atoms can fall to the other ground level and be lost to the transition altogether — optical pumping, which the model leaves out and which deepens every hole the pump burns. The positions do not depend on any of that: the separations between the features are the hyperfine splittings of rubidium's excited state, read to a fraction of a megahertz in a glass cell on a bench.

The lines a warm vapour hides

Shine a tunable laser through a cell of rubidium vapour and the absorption is one smooth hump half a gigahertz wide, though the atoms' own lines are eighty times narrower and three of them lie inside it. The atoms are moving, each sees the light Doppler-shifted by its own speed, and their lines are smeared together. Send a second, stronger beam back the other way and narrow dips appear in the hump at exactly the frequencies of the hidden lines — because only atoms standing still can be talked to by both beams at once. The vapour stays at room temperature and the motion is not removed; it is selected against.

quantum · Atomic spectra The deeper the line, the closer to gravity. The shift of a solar line in sunlight seen from the Earth, against the line's depth, in the two-stream model with the convective velocities dying away above the photosphere over 150 km and a deeper line taken to form higher (600 km × depth²). Weak lines, formed low among the fastest flows, show 411 m/s — about two-thirds of the gravitational value; the deepest lines, whose cores form in the upper photosphere where the granules' motion has nearly stopped, show 627 m/s and are still climbing towards the 633 m/s that gravity alone gives, drawn as the dashed line. That is the measurement made with integrated sunlight reflected from the Moon and calibrated with a laser frequency comb: plot the shift against line depth, and read the gravitational redshift off where the strongest lines are heading. Its published value, 638 ± 6 m/s, agrees with general relativity.

The redshift the Sun's boiling hides

Light leaving the Sun climbs out of a gravitational well and should arrive redder by 633 metres a second in velocity terms — a prediction Einstein made in 1907, before he had general relativity. It took half a century to confirm, and the reason was not the size of the effect but the Sun's surface, which boils. Bright hot gas rising in granules and fainter cool gas sinking between them blueshift every line by a few hundred metres a second, by an amount that depends on the line and on where on the disc it is seen. The gravitational shift was found by treating that nuisance as a second measurement: deeper lines and lines near the limb both converge on the same number.

astrophysics · Gravitational redshift

Named alongside it

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

Angular momentumAtomic spectraDegeneracyEnergy levelsFine structure constantGravitational redshiftMagnetic momentSelection rulesSpinChandrasekhar limitCompactnessConvective blueshift

All concepts