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I understand that different atoms have different ground states, but when we are asked questions, where the ground state is not n=1, will the ground state always be given or are there ways to solve for it?
They are sometimes given, but other times the problem might just mention the presence of ultraviolet or visible light. A hydrogen atom producing ultraviolet light is part of the Lyman series and thus the ground state is always 1, so n1=1. Meanwhile a hydrogen atom emitting or absorbing visible light is part of the Balmer series in which the initial ground state level is always 2, so n1=2. So if the numbers aren't given look out for what type of light is produced and you will at least have one of the energy levels.
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