Is the blue color of a flame caused by continuum or line emission?
In most books you will find that the color of a candle flame is identified as being continuum emission, as opposed to 'line emission' in which you can clearly see dark spaces between a few lines in the dispersed light from the light source. At the level of the constituents of the flame, the process becomes more difficult to describe.
The major constituent of a candle flame is soot. Physicists are only now beginning to understand just what soot is, and how it forms. It is believed that it is initially composed of fragmented carbon super-molecules containing dozens of carbon atoms linked together into plates and filaments of one kind or another.
Quantum mechanically, such ensembles have a large number of quantum states that they can radiate energy from, either from emission from individual carbon lines, or from the innumerable vibratory modes of such large coherent ensembles of atoms. Taken together, all of these quantum states produce so many lines across the visible spectrum that the soot particles effectively look like tiny 'black bodies' that operate pretty much the way large pieces of iron do when heated, but the effective temperature of these states is lower than the corresponding black body would have to be to give the same color.
The various colors of the flame represent regions of the escaping soot cloud heated to temperatures such that the warm particles emit most of their energy in the quantum states towards the blue end of the spectrum. The other colors are produces by soot particles emitting in the other quantum states of the carbon molecule which are located in the yellow and orange parts of the visible spectrum.
The effect of the crowding together of the quantum states in the visible spectrum is that the emission from the soot LOOKS like a continuous spectrum; but at very high resolution with a spectroscope, the emission would break up into thousands of closely spaced lines.
Candle flames are only about 700 F hot or so. The color does not come from black body emission because 'red' would indicate black body temperatures of 2000 K, orange of 3000 K and yellow of 6000 K. Clearly such temperatures do not occur in candles, so the color has to be explained by the quantum nature of the line emission from soot particles.
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