Sean Silver explains how Prussian blue works:

"The iron in Prussian Blue is in two different oxidation states – which is to say, has two different numbers of electrons. As iron(II), it has given up two electrons, and is a dark brown color. Iron(III) [where it's given up 3 electrons] is rust-red, precisely because rust is mostly composed of iron in that third oxidation state.

The ability of iron easily to switch between oxidation states happens to be what makes it crucial to blood – and makes blood visibly different when oxygenated. When the iron(II) in hemoglobin forms a bond with oxygen, it gives up an electron to become iron(III); it changes its oxidation state, and becomes bright red. That same compound will later give up its oxygen to a cell which needs it, reclaiming its electron and reverting to duller, darker color gained from iron(II).

The blueness only happens when both ions are locked in close proximity, from a special process called intervalence charge transfer. When hit with light of the right wavelength, some of the iron(II) ions throw off an electron, which is captured by a neighboring iron(III). Though the individual atoms stay locked in the lattice, the ions switch places, one shedding an electron, which the other gains. Because the compound absorbs only the precise orange wavelength that triggers the charge transfer, it reflects everything else. In white light, our eyes register the sum of the reflection as blue."

The picture shows how it works. But I don't quite get it: some irons touch 6 carbons and others touch 6 nitrogens. Is that why some are iron(II) and some are iron(III)? If no atoms move in this "intervalence charge transfer", that can't be right.

(2/n)

@johncarlosbaez

I understand how the two valences of iron give rise to the two different colours (dull brown and bright red) of blood. But then you say that when the two are in close proximity, this can look blue, and I'm half expecting you to say that this is why veins look blue through the skin. But that seems like a little too much; it's just a coincidence, right?

@TobyBartels - wow, interesting - I really have no idea! Let's see if I can look up something about "blue blood".

This article says it's not the blood itself that's blue:

"It is true that veins, which are sometimes visible through the skin, may look bluish. Why should this be so? Click here if you want the full story. But the short of it is this: It has to do with the way tissue absorbs, scatters and reflects light. (I think this also explains why your lips look blue when you get cold.) But if you were to open one of your veins, or cut your lip, even when you're cold, there'd be nothing blue at all about the liquid that would pour forth.

Maybe it is the fact that veins look bluish that explains the myth that blood is blue as it flows through the veins?"

(The link at "click here" is broken.)

https://www.npr.org/sections/13.7/2017/02/03/513003105/why-do-many-think-human-blood-is-sometimes-blue

@johncarlosbaez @TobyBartels

Somewhat relevant but still unsatisfying explanation of blue veins. I’m still missing the part of the explanation that says why veins should ever reemit more short wavelength photons than long.

http://www.abc.net.au/science/articles/2014/11/04/4120712.htm

@wlumley

I think you just blue yourself there Will