I How does atomic absorption spectroscopy work

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If electrons absorb light, how can the spectrometer detect those wavelengths?
I did a prac where we tried to calculate the rydberg constant for hydrogen. We had a hydrogen lamp and we used a spectrometer that was hooked up to a photomultiplier tube to detect the wavelengths of light corresponding to the balmer series. In one section I need to write up a brief summary of how the experiment works, but I don't fully understand it. The explanation in our lab doc says light from the source is diffracted by the spectrometer and focused onto an exit slit so that only a particular wavelength of light can be transmitted to the detector at anyone time. Are we measuring the emissions of the electrons? If not, then what are we measuring? It can't be the lack of spectral lines since our PMT showed spikes in intensity at wavelengths that correspond to the balmer series. If we are measuring the emissions why isn't this just atomic emission spectroscopy?
 
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Is there some kind of schematic in the lab instructions?

It could be that you are measuring the reemission from the atoms, which will happen when the incoming light is resonant. It would still be absorption spectroscopy as the light source is monochromatic. From emission spectroscopy you would excite the atom thermally and analyse all emitted light to see which wavelengths are being emitted.
 
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