What is the relationship between the absorption spectrum and the corresponding emission spectrum of light?
Theoretically the two should be very similar; i.e., a given gas should show absorption lines at the same wavelengths that it shows emission lines. Not simultaneously, of course; the absorption lines occur when broadband (i.e., white) light passes through a thickness of gas, while the emission lines happen when high-energy photons hit a quantity of gas and its orbital electrons do an up-down dance, jumping to some high level on absorption of the photon energy and then emitting as they jump downward in discrete steps.