First of all, let’s think about what paint is. At a minimum, paint is a combination of a binder (some material that dries to form a film, like acrylic or oil) and a pigment, some material which gives it a color. A pigment is a material which absorbs some colors of light and reflects others; most pigments are minerals. (There are also organic pigments, such as the Imperial Tyrian purple made from the snot of the Murex snail, but not as many, and they tend to be much more expensive for the simple reason that there are a lot more rocks than there are animals and plants.) So for something to be a cheap pigment, it has to be a good pigment, and it has to be cheap. So let’s figure out what makes each of these happen.
To be a good pigment, first and foremost, something has to have a nice, bright color. The way pigments produce color is that light shines on them, and they absorb some, but not all, of the colors of light. (Remember that white light is a mixture of many colors of light) For example, red ochre, a.k.a. hematite, a.k.a. anhydrous iron oxide (Fe2O3), absorbs yellow, green and blue light, so the light that reflects off of it is reddish-orange. (This happens to be the pigment that’s used in barn paint, so we’re going to come back to it.) Light is absorbed when a photon (a particle of light) strikes an electron in the pigment and is absorbed, transferring its energy to the electron. But quantum mechanics tells us that an electron can’t absorb just any amount of energy: the particular energies (and therefore colors) that it can absorb depend on the layout of the electrons in the material, which in turn depends on its chemistry.
The detailed calculations, or even the not-so-detailed calculations, are way beyond the scope of this post. (There are even whole books about it, like Nassau’s The Physics and Chemistry of Color) But there’s one important pattern which I can at least tell you about, which is that if you look at the various atoms which form a pigment, and you look at their outermost electrons (not the inner electrons, which are so tightly bound to their atom that they don’t participate in chemistry; all of chemistry is determined by the behavior of the outermost electrons around an atom) then it turns out that certain kinds of outermost electrons form pigments, and certain ones don’t.
The magic property is what’s called “angular momentum,” which basically measures how fast these outermost electrons are rotating around the nucleus. Electrons in atoms get angular momentum only in fixed increments (there’s that quantum mechanics again, only fixed increments allowed) and for historical reasons, the first few increments are named “s,” “p,” “d,” and “f.” On the periodic table, (http://www.webelements.com) the elements whose outer electrons are “s” form the two tall leftmost columns; the “p” elements are the big square on the right; the “d” elements are the big block in the middle; and the “f” elements are the two rows off at the bottom. (If we ever make element 121, it would be the first “g” element)
Electrons with less angular momentum spin in more spherical (rather than deformed) orbits, and when multiple electrons are trying to fly in the same spherical orbit, they repel each other pretty strongly. The result of this is that two “s” electrons meeting will have very different energies — and it turns out that, in quantum mechanics, the amount of energy an electron can absorb is exactly thedifference between these energy levels. So “s” means a big gap, “p” a slightly smaller one, and so on. And it turns out that “d” electrons are right at the sweet spot where that gap corresponds to visible light.
Well, why are those particular colors of light visible? It’s because of the temperature of the Sun: our eyes didn’t evolve to see X-rays because there aren’t many X-rays to see around here. Instead, they’re very sensitive in the range of colors that the Sun produces, from red (around 780nm wavelength) to a peak brightness of yellow (around 600nm) all the way up to violet (around 400nm). Those colors correspond to energy gaps of about 0.3 electron volts (eV, a good unit of energy for studying atoms) which are right around the energies of chemical bonds involving d electrons. S- and p- bonds involve energies of 1-3 eV, corresponding to wavelengths around 100nm, in the far ultraviolet range.
Did we just get lucky that the Sun is yellow, and if we lived orbiting another star might the useful pigments come from p bonds? Surprisingly, the answer is no. The Sun’s color comes pretty directly from its temperature: it’s literally glowing yellow-hot, with a surface temperature of about 5,800K. The coolest stars, red dwarfs, are about 2,800K and glow red. The hottest stars, the type O stars, go up to about 40,000K, only 72nm; but it turns out that when a star gets any hotter than class F (about 7,000K, about 400nm — blue) its lifespan starts to decrease precipitously. This is because the temperature of stars is actually fixed by the kinds of fusion reaction going on in their core, which I’ll get back to in a moment, and those hotter reactions burn through their fuel a lot faster. The net result is that any star that’s going to last long enough to have planets with life on them might be a bit redder or a bit bluer than our sun, but not radically so: and it’s those d-orbitals that are going to make the best pigments for anyone whose eyeballs evolved there.
Red ochre (Fe2O3) is a simple compound of iron and oxygen that absorbs yellow, green, and blue light and appears red. It’s what makes red paint red. It’s really cheap because it’s abundant. And it’s really abundant because of nuclear fusion in dying stars: