or you can just watch this:
Sorry to be that guy, but 6 year olds arenât toddlers.
Nice article, though!
I know. The series title started with a question from an actual toddler, but quickly expanded to mean âyoung childâ.
While it may be intuitively useful to simply frame the issue as derivative of simple single bond motifs, it is actually only the beginning of the discussion. The scientific model you described here is just too simplistic and at times the language you used here is also somewhat incorrect. I will explain.
There are no molecules in diamond or graphite. Those are networked or sometimes crystalline or semicrystalline materials, and under certain conditions and with certain structures, some allotropes of carbon (like when you have graphite, nanotubes, or buckyballs) can demonstrate delocalized electron bonds across a lattice of atoms. The molecular orbital approach that is useful in singular molecules thus becomes more extended and sophisticated by material scientists into what is often called a âdensity of statesâ. Then, after you know something about the density of states you add light to that density of states, and try to propagate it with equations derived from Maxwellâs Equations and then things become even more complicated, and thus fall outside of guidance of molecular orbital theory.
The total (often impure) band structure (reflecting the density of states) of a regularly arranged (on an atomic level) material and how light interacts with that band structure is what gives a solid material its sophisticated color. This is inherently difficult to model with consideration to irregularly placed impurity atoms; and, the model that material scientists use to predict color and appearance does not always involve absorbing photonsâŚsometimes photons are scattered, sometimes they are re-radiated, and sometimes they are thermally generated by black body radiation (which involves mere kinetic vibrations of atomic material and can be independent of the light you hit the material with). Itâs therefore not really the mere existence of individual Pi bonds an Sigma bonds summed together, itâs the way in which electrons populate the available electron density of states at a temperature and pressure relative to the way in which light can permeate or navigate those density of states. This also incorporates the notion of a âskinâ depth of a materialâs crystal where the density of states has to contend with altered surface electron states which can cause reflections and other color propertiesâŚwe have to worry about surface states more so with other materials, for another example, nanocrystalline quantum dots.
In summary, light scattering, light adsorption, etc, all of these physical phenomena are very complicated processes (often governed by an interplay between quantum mechanics and maxwellâs equations) regulated by how the density of states (if applicable, i.e. for extended materials) across the material disturbs the propagating electromagnetic field found in light.
You might look up the âband gapâ differences (gaps of energy within a density of states) between classes of insulators, a conductors, and a semi-conductors to see that often there are virtual states and impurity states within the density of states that mess things up for simple light propagation modelsâŚeven in things like allotropes of carbon.
Thanks for stimulating the topic though. Science is deep. 
After wading through the big words and âgee-whizâ science, the answer seems to be, still, âNobody actually knows.â
I found this question from a different angle to be very helpful when understanding transparent vs opaque. And colors. Other folks might appreciate this approach too.
âWhy shouldnât photons go on through solids?â
We think of solids as, well, solid. But really they are mostly space. 99.999(and a bunch more 9âs)% space. So why wouldnât a photon just slide on through? Electron orbital states to the rescue. If a photon gets near an atomâs electron, it can make the electron jump states. Jump to a higher orbit. Â The photon is absorbed in the process. But only if there is a close enough match between the energy of the jump and the energy of the photon. The gap you spoke of.
If there isnât a close match, the photon just keeps on goinâ.
Every substance has different gaps. If they are gaps that match visible photons, those colors are absorbed. For diamond, none of the gaps match visible photons. For graphite, all of the gaps match. For rubies and blood, non-red colors are absorbed. For emeralds and leaves, non-green is absorbed. And so on.
No, actually, this is a very well understood problem. You canât calculate everything from first principles (we donât have a full many-body solution to any quantum mechanics problem) but you can get pretty darn close. (Iâm using a lot of classical language below but I think it is good enough).
In a typical first semester undergraduate quantum mechanics class, you may spend a month on the hydrogen atom. Classically, the attraction strength of a proton falls off quadratically with distance (because space is three dimensional). Call that a âCoulombic potential well,â toss it into the Schroedinger equation, and a few careful pages later, out pops the allowed energy states for hydrogen - discrete energy levels, and the shapes of the orbitals of those energy levels. Spend a few more days making corrections for relativity, magnetic interactions, etc. Add a second proton and you get the energy levels of helium (almost - the second electron screws things up enough that you canât get an exact answer from first principles). And so on. In practice, for larger atoms you measure the energy levels experimentally - shapewise they look almost just like those for hydrogen, but the energy differences vary.
What if you bring 2 hydrogen atoms together? If 2 hydrogen atoms are non-interacting (infinitely far apart) then they both have identical energy levels. Imagine bringing them closer together. The equations now allow for the possibility that both electrons are near one proton, or the other, or one near each. Remember, mathematically an electron is a wave the square of whose amplitude tells you the likelihood of finding it at that point. If an electron is at the lowest energy (ground) state derived for one hydrogen atom, it can âleakâ a bit of itâs wave-function into the ground state of the other - turns out there are a few ways to do this mathematically to get different states for the new âtwo coulombic wellâ potential. Turns out one of those has lower energy than an isolated hydrogen atomâs ground state, and one has higher. The lower energy state has the electron mostly between the two protons (a bond) and the higher energy has it on both sides with the protons in the middle (anti-bond).
What if you have a crystalline solid - a periodic array of coulombic potentials? The same thing happens again and again and again as you add more atoms, and the individual, discrete states of single atoms get mathematically mixed in very specific ways. The discrete energy levels become bands of allowed energy levels separated by band gaps. You have to make a few approximations because the math is harder, but it works. This is the basis for all semiconductor device physics - you can readily derive diodes, transistors, LEDs, lasers, etc. this way.
Remember that light comes in photons with specific energies. Blue light has higher energy per photon than red. Photon energies less than the band gap canât be absorbed, because an electron that absorbed it wouldnât have a state of the right energy to go to (it would end up in the gap). Diamonds have a wide bandgap, and can absorb UV but not visible light, so theyâre clear. Graphite has a different crystal structure (different arrangement of atoms) and so a smaller bandgap.
This also explains colored diamonds. Add impurities like boron or nitrogen, and those atoms replaces carbon at some points in the crystal or end up where there shouldnât be atoms at all. This breaks the periodicity and can introduce states where youâd normally have band gap. The crystal can now absorb lower energy wavelengths because electrons can jump into the states caused by defects.Different defects make different new states. Because impurities can have more or fewer valence electrons than carbon, they can also increase electrical conductivity. In electronics, the process of adding impurities is called âdoping.â The change in electron density can also have an effect on the band gap. See http://www.webexhibits.org/causesofcolor/11A0.html
âBecause when Superman compresses the coal down in his titanic gripâŚâ
Well! Iâm glad we got that straightened out!
Lots of very bewildering metaphors in the article and the comments but no illustrations. Hard for me to follow whatâs going on.
If the color is decided by which kinds of photons it âthrows offâ, what explains reflectivity vs transparency? Actually, what the heck distinguishes âtransparentâ, âwhiteâ, and âreflectiveâ ?
Reflectivity vs transparency is essentially defined by what happens when photons from a light source interact with the material.
If the photons pass through the material without being absorbed by any molecules, the material is transparent. If the photons bounce off, itâs reflective. The more unevenly the photons bounce off (e.g. because the surface is not perfectly smooth) the more the light is scattered in all directions and the material appears white.
Colours come about because for many materials, photons with different amounts of energyâi.e. having different wavelength, which we perceive as colourâare absorbed or reflected differently by the material:
For example, a red material might absorb any high energy photons but reflect lower energy red photons. When those reach our eye, we see red. A green material would absorb the red and blue ends of the spectrum but reflect the green in the middle. (There are other ways that colour come about but thatâs the gist of it).
Something that appears âblackâ to us does so because all wavelengths in the visible spectrum are absorbed rather than reflected.
âThereâs a reason you donât want to live next door to a coal-fired power plant and that reason is all the nasty stuff that gets released when the carbon in coal burns.â
Because they donât use scrubbers or any other technology to clean the exhaustâŚ
They do. Itâs still not clean. Check out the stats on asthma and chronic disease rates in downwind areas.
Maggie â Iâm confused by your language. âDiamonds and coal are different colors because coal isnât pure carbon.â âLike diamond, graphite is carbon. Unlike diamond, itâs a shimmery, silvery black.â My brain is exploding now. Both statements can not be true. âSo itâs not really that diamonds are clear.â If diamonds arenât clear, I donât know what clear means. Why make this topic more complicated than necessary?
Regged here to comment, because of â[âŚ] like toddlers on a tether.â (Rly annoyed the heck outta me :))
Perhaps adhering to some âstandardsâ, but surely ridiculous ones. :-/
Coal isnât Graphite.
But itâs black for the same reason
Pretty much, yeah.
