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Why does Butane burn blue? From my (very) basic understanding of chemistry, carbon and hydrogen do not burn blue, their radiation spectra are different-so why should the combination burn blue? Please elaborate as much as possible, about bonds, orbitals, electrons, and the like!

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The blue flame from butane (or many other hydrocarbons) is due to the complete combustion of the gas. From the Wikipedia article Flame color it mentions,

In the most common type of flame, hydrocarbon flames, the most important factor determining color is oxygen supply and the extent of fuel-oxygen pre-mixing, which determines the rate of combustion and thus the temperature and reaction paths, thereby producing different color hues.

Specifically, making the link to the common tool in the laboratory, a Bunsen Burner, which typically has two 'types of flame (as seen below):

enter image description here

Image Source - which states that:

The Bunsen Burners we use at school use a mixture of alkane gases like propane and butane

The yellow flame is from an incomplete combustion, producing $\ce{CO}$ and the colour is due to (according to the Wikipedia article):

incandescence of very fine soot particles that are produced in the flame.

With more oxygen, a complete combustion of butane is possible (without the soot):

$$\ce{2C4H10 +13O2 -> 8CO2 + 10H2O}$$

Which provides

enough energy to excite and ionize gas molecules in the flame.

and the blue flame colour is due to the

emission of excited molecular radicals in the flame, which emit most of their light well below ~565 nanometers in the blue and green regions of the visible spectrum.

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The blue color is the Swan lines' emission of $\ce{C2}$. Rather than acetylene diradical it is more likely to be the olefin singlet dicarbene,

enter image description here

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