1. Single atom spectrum
If we consider carbon as a single atom then it emits all over the visible light spectrum. There are emission lines in red,yellow,green,blue indigo & violet colors. With carbon there's a complete rainbow of colors. By applying corresponding energies(electrical,heat,mechanical it doesn't really matter what kind of energy)specific color lines would be obtainable in carbon.
2. Graphite vs diamond vs diamond like carbon
Practically speaking however we don't really find one atom of carbon floating around displaying its vivid colors. Carbon atoms arrange themselves into a dark black graphitic form or a transparent diamond form. Already we have two extremes of optical properties in a single element.
But there's also diamond like carbon. In this form due to functionalization the bond angles of hetero atom-decorated carbon starts to look like that of sp3 diamond. Consequently its properties tend to shift towards diamond as well. It becomes optically transparent. It acquires a band gap. It becomes harder(than graphite). But its not yet a complete diamond so retains the properties of both graphite & diamond. One could say that Diamond like carbon assumes a middle ground between graphite & diamond.
"What about glassy carbon"
Glassy carbon is graphite like in its optoelectronic properties.However its properties vary so much due to precursor used,synthesis time that its next to impossible to say anything for sure.
3. Effects of doping
Carbon can't be doped in a traditional sense.It forms chemical bonds with almost every element of the periodic table,except for noble gases.Many researchers equate intercalation with doping but those two are different from each other. So we can't comment about the effects of doping on optical properties of carbon.
4. Effects of functionalization
Carbon has a very rich chemistry & can be easy functionalized with different atoms. As a general rule with increasing degree of functionalization(on a graphitic backbone) its band gap tends to increase proportionately until it becomes completely transparent like diamond.
5. Carbon stars
Carbon stars are not all carbon stars. There are other elements present in huge quantities(greater than carbon content itself) so the emission spectrum observed from these entities is not really representative of carbon as such. Furthermore these stars are often surrounded by a layer of soot that is very close to a perfect black body & hence absorb a significant portion of light falling on them.And frankly considering how the universe is full of dust it is hard to take spectroscopic data of space bodies seriously. It is best to ignore it completely.
6.Black body properties
Carbon nanotubes like soot are as close to a perfect black body as there can be. They absorb a wide spectrum of light in UV,visible,IR,and microwave domains. On the flipside these materials also emit in the same domains they absorb from
A perfect black body is also perfectly emissive,in other words if energy is applied to a black body it will radiate pure white light.Carbon follows this trend as it has been shown that a suspended graphene sheet emits white light on application of electrical energy in a pattern similar to that of BBs.
https://www.pnas.org/doi/10.1073/pnas.0900155106
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