Apparent color of flame as superposition of spectral lines?

Question

In some cases one can identify a substance by the color emitted as it burns in a flame. A green flame might indicate the presence of copper. So here is the question.

If we know wavelength and intensity of emission spectra for an element, isn't what we "see" as it burns simply a superposition of these? If I try to reconstruct the apparent color of copper from its spectrum as $\sum f_n \cdot i_n /\sum i_n$ in which $f_n$ and $i_n$ are the frequencies and relative intensities respectively, it seems to work. But trying this with, say, helium, using approximations because there are a lot of lines, I consistently get something in the green range.

This site gives a simplified spectrum for helium in a tube. Approximating the intensities I get something in the green range. I tried a more detailed calculation using selected NIST data and obtained a similar result. But helium is consistently shown as having a red appearance in a flame or in a tube (link).

One guess is that there are invisible emission lines, and helium has many. If these are included in the sum they might drag the apparent color toward the red.

Is my basic understanding incorrect? Any insights appreciated.

Answer 1

If we know wavelength and intensity of emission spectra for an element, isn't what we "see" as it burns simply a superposition of these?

Yes.

If I try to reconstruct the apparent color of copper from its spectrum as $\sum f_n \cdot i_n /\sum i_n$ in which $f_n$ and $i_n$ are the frequencies and relative intensities respectively, it seems to work. But trying this with, say, helium, using approximations because there are a lot of lines, I consistently get something in the green range.

Actually, that's not how to interpret it. What the above is doing is adding together frequencies, but that's not what it means to have a "superposition of emission spectra". The flaw becomes obvious when you consider a flashlight. If you shine red and green light on a wall, is that the same as shining ultraviolet light on the wall? No, you just get a mixture of red and green photons hitting a wall.

Similarly, emission spectral lines do not add their frequencies to form a single frequency, but rather they coexist independently. Helium glows reddish because the dominant visible lines are red and yellow.