Flame emission colours

Why does each metal give a firework its own colour instead of all of them simply glowing hotter?

Drop a pinch of table salt into a gas flame and it turns a flat, insistent yellow. Drop in a lithium salt and the same flame turns crimson. The temperature has not meaningfully changed, and the two salts sit in the same column of the periodic table. So the colour is not reporting how hot the flame is; it is reporting what is in it.

That should be surprising. Heat a poker and it glows red, then orange, then white — colour tracking temperature, exactly as you would expect. Why do these flames refuse to follow that rule?

Notice there are two different ways an object can send out light, and the poker only shows you one of them. A hot solid radiates because its enormous number of jostling particles have an almost continuous range of energies available to them; the light comes out as a smooth spread across all wavelengths, whose peak shifts with temperature. That is thermal, or blackbody, radiation, and it is why star colours track their surface temperatures rather than their compositions.

Now take a free atom in a flame — a sodium atom, alone in hot gas, no longer part of a crystal. What energies can its electron have? Not any energy at all. The bound states of an electron in an atom are quantised: a small set of allowed levels with definite gaps between them, and nothing in between. That is not a rule invented for flames; it is the same quantisation that makes the atom stable in the first place.

Follow the consequence. A collision in the flame can shove the outermost electron up to a higher allowed level. It cannot sit there — typically within nanoseconds it drops back, and the energy it sheds leaves as a single photon. The photon's energy is fixed by the gap, and a photon's energy fixes its wavelength. Sodium's outer electron falling from the 3p level to 3s releases about 2.1 electronvolts, which is light at 589 nanometres: that particular yellow, and no other.

So ask what determines the gap. The arrangement of levels depends on the nuclear charge and on how many electrons are already there screening it — which is to say, on the element. Two elements have two different ladders, so they cannot emit the same set of wavelengths. The colour is a signature, not a temperature reading.

And notice what this predicts about the shape of the light. Because only certain gaps exist, the emission is not a spread but a set of narrow lines. Put a sodium flame through a prism and you do not see a rainbow with a yellow bulge; you see a dark field with a bright line in it — in fact two, at 589.0 and 589.6 nanometres, split by an interaction between the electron's spin and its orbital motion. That doublet is why sodium street lamps render colours so poorly: emitting at essentially one wavelength, they leave an object with no yellow in it nothing to reflect.

Does raising the temperature change the colour, then? It changes the brightness, because a hotter flame excites a larger fraction of the atoms, and eventually opens up higher-energy transitions that were rarely reached. What it cannot do is move a line, because the line is the gap and the gap belongs to the element.

Three refinements are worth making, because the tidy story above is a simplification in each of them.

First, the flame colours of fireworks are often not free-atom lines. Sodium's yellow and lithium's crimson are genuinely atomic, but the deep green of a barium star and the red of a strontium star come mostly from short-lived molecules — barium monochloride and strontium monochloride — formed in the flame. Molecules have vibrational and rotational levels layered on top of the electronic ones, so they emit clusters of closely spaced lines that read as bands. That is exactly why pyrotechnicians add chlorine donors: the point is to manufacture the emitting molecule, not merely to deliver the metal.

Second, the atoms are not what you loaded. You put in a salt, and the flame's heat has to break it apart before there is any free atom to excite. Elements whose salts are hard to break, or whose excitation gaps are too large for the flame to reach, give feeble colours or none.

Third, the continuum has not gone away. Any real flame contains hot particles — soot, incandescent metal oxides — radiating thermally underneath the lines, and a firework's brilliant white is deliberately made that way with burning magnesium or aluminium. Line emission and thermal glow run at once, and a formulation chooses how much of each it wants. That connects back to a companion question here, why stars have different colours: a star's colour is overwhelmingly the continuum channel, set by temperature, while the lines superimposed on it are what tell you the composition. Read the continuum for heat, the lines for identity.

• How the same set of transitions appears as dark absorption lines when light passes through cooler gas, as in a stellar spectrum.
• Why some elements need the far hotter plasma of an inductively coupled torch before their lines appear at all.

Every term the collection defines is gathered in the glossary.