During a flame test, we excite the electrons in an atom to a higher energy level, and we observe their relaxation based upon the light (color) spectrum emitted by the relaxation process. In general, we usually observe only the spectra of the metal, or the cation, in the flame test because most nonmetals tend not to emit in the visible spectrum.
The anion may also have low excitation efficiency, so that there are just fewer electrons excited and relaxing and thus less intense light emitted. Because of this, the color observed comes from the metal cations most of the time. You can still sometimes see the influence of the anion used on the emitted spectrum; for instance, CuBr2 will yield a blue-green flame, while CuSO4 will have a green flame. Any electron can be excited out of its state to a higher energy state; however, we view only valence or close to valence energy transitions with the flame test because there is not enough thermal energy to excite one of the core electrons. The core electrons require something with energy on par with an x-ray to be excited to a higher state, as they are tightly bound to the nucleus.
I've always liked the flame test, myself! It has a lot of pizzazz. Though I don't remember the lesson before or after my first flame test, I remember watching it for the first time. If anything, it is memorable. Best of luck!
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