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I know that the aim of atomic spectroscopy is to measure the energy emitted or absorbed by monitoring photons, and the photoelectric effect studies the kinetic energy contained by electrons after incident light exceeds the work function. Why doesn't the energy added to the atom in atomic spectroscopy excite the atom enough to leave completely? If there are different energy levels for the electron to jump to, does that just mean the photoelectric effect is what happens when n goes to infinity?
The photoelectric effect is not when n goes to infinity because the energy of the photon subtract work function = kinetic energy. Kinetic energy can vary and does not mean that the electron has separated from the atom. The electron could have traveled between certain orbitals and not out of the atom.
In atomic spectroscopy, the electron doesn't completely leave the atom because it is still being pulled towards the positively charged nucleus of the atom. Also with the photoelectric effect, the detector that detects the speed of the ejected electron is slightly positively charged so it'd draw the electron to it.
I also believe that in Atomic Spectroscopy, the goal of the experiment was to determine at what energy levels of photons, will electrons of specific metals become excited to then release the energy. This experiment for Atomic Spectroscopy was more of a verification of the shell model for atoms while the Photoelectric experiment was a verification that light can have both wave and particle properties.
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