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Electrons in the outermost shell have the greatest amount of energy because they are the farthest from the nucleus. These electrons are experiencing less of a pull to the positive nucleus; therefore, have more energy.
Both are similar in that they detect electron movement as a response to light. However, the photoelectric effect has to do with electrons actually being emitted, meaning photons have to be at a sufficient energy level. Atomic spectroscopy on the other hand can observe in-between states.
Electrons in the outermost shell have the greatest amount of potential energy because as we know potential energy is defined by energy which an object has because of its position/location, also referring to energy from net electrical charge or stored. Therefore in order to move an electron from an innermost shell to an outermost, a large amount of energy is needed which in turn results to high potential energy for electrons in the outermost shell.
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