Okay, so green is green because it’s reflecting green.
Right?
Well, why is it reflecting green? Why doesn’t it reflect something else? Like red?
Because then it would be red. Really. The colour of something is defined by what colour light it reflects into your eye.
If you’re asking why any given material reflects one colour and not another, well, the answer is almost as varied as the possible materials the thing could be. Basically the material it is composed of, and the surface texture, means it absorbs certain wavelengths and consequently reflects all others.
Wavelengths of light are absorbed differentially by different molecules based on things like distance between atoms, electron energy levels, etc, etc. Some photon wavelengths will be absorbed, others will not.
“It’s reflecting green” really means “it’s absorbing red and blue light more than it’s absorbing green light”, simply speaking.
So the object contains some molecules that absorb red light, and some that absorb blue light, but relatively few that absorb green light. As smeghead said, that’s all to do with atoms and stuff. (Or to be more precise, electronic energy levels.)
Here’s a handy page if you want to know more: http://en.wikipedia.org/wiki/Absorption_(electromagnetic_radiation)
If one had a given molecule, could one figure out its color based on its chemical (atomic, etc.) composition, without ever actually looking at it?
For example, certain elements have been created in the lab, but lasted only instants before decaying, and only a few atoms of it at that. Could one calculate what it would appear like, IF we had a large enough sample to look at?
Not always. Some materials appear the color they do because the pattern in which they are arranged causes interference, so analyzing reflectance and absorption patterns of individual molecules wouldn’t tell the whole story.
For example, depending on particle size and surface treatment, iron oxide can be black, red, brown, or…er, rust-colored.
To some people, they do look the same.
Can said persons tell us whether they are seeing green or red then? Asked with tongue only slightly in cheek…
Even neglecting solid structures and molecular interactions this is still pretty difficult to do, but the calculations can give you a pretty good idea if you use the right programs. The trouble is molecules are always in motion so the electronics are allways slightly changing. You may be able to calculate that a molecule will absorb at around 500nm, but it would be extremely difficult to calculate how broad that absorption band is. If you know other similar molecules, you can make a very good educated guess.
With the short lived elements, you are generally dealing with coordinated complexes or the free ions. The absorption bands of these atoms might be easier to predict with Tanabe-Sugano diagrams. I’m not sure how well they work for the F-block elements though, but there may be an F-Block equivalent.
These methods are only useful for solution or gas phase color though. As has been mentioned, crystal structure can create macroscopic properties that change the observed color.
Many things are yellow or orange or red or brown because they have a tendency to reflect only the light with wavelengths longer than some limit. This has to do with the way small structures disorganize shorter wavelength light and absorb it into heat rather than letting it reflect or transmit. For this reason, these colors are more common in nature. This tendency is true in the ultraviolet, also, though we don’t notice it by sight. For many things this tendency increases with time, so they get less reflective in the ultraviolet, then in the blue, and so forth. We see paper yellow with age, and our vision yellows, too.