What molecules are produced in carbon arc lamp and how do they produce light?
Answers:


Consider the mass and kinetic energy of an electron or of an ion of nitrogen or oxygen, and the reactivity with carbon.
Good question! It would be interesting to see the relative abundance of allotropes of carbon deposited from a filament in vacuo. There is a metallic glisten to the deposit, so there might be graphite, carbon nanotubes or buckminsterfullerene. $\ce{C2}$ would not be there for long, though.
There are a great many chemical species produced by an arc lamp operating in air. Depending on the gases in which it operates, an arc can produce complex organic molecules. Even something as ornate as a buckyball can be made!
I've not seen the relative abundance of products of an arc lamp, but I assume carbon oxidizes rapidly to the monoxide and dioxide, depending on abundance of oxygen. Charcoal briquets oxidize at a far lower temperature.
Most of the light is black-body radiation, though there would also be some spectral lines produced by recombination, such as from nitrogen. With a spectroscope, you'd see a continuum with a few bright lines added (or dark lines from absorption, as the gases cool).