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I had a question regarding the "excited state" of electrons. I know that electrons can jump up from their ground state to higher energy levels if given a specific amount of energy. But what if the electron is already excited state? Can it still absorb more energy (the right amount) to go up higher or is there a rule that states that it must come down to the ground state first before going up again? And if there is, why?

This query popped up because I watched this video.

If you go to the timestamp of about 10:30, he states that the emission spectrum will not be the same as an absorption spectrum for the same element. (I thought that the emission spectrum is the same as the absorption spectrum).

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I know that electrons can jump up from their ground state to higher energy levels if given a specific amount of energy.

This statement confuses a semi-classical model (Bohr model of atoms) with the final quantum mechanical solution for the atomic physics spectra. The Bohr model has been superseded by the solution of Schrodinger's equation. The solutions for the Hydrogen atom are the same as for the Bohr model, but it is not the electrons that gain and lose energy with the absorption and emission of a photon but the whole atom.

Quantum mechanics solutions give the probability of interaction, so one cannot talk of electrons jumping . When a photon is absorbed the QM true description is " the atom exists with an electron in an orbital of a higher energy state". The Bohr orbits are an approximation to the statistical accumulation of the orbitals .

But what if the electron is already excited state?

This should be " But what if the atom is already excited state? "

Can it still absorb more energy(the right amount) to go up higher

yes

or is there a rule that states that it must come down to the ground state first before going up again?

No such rule.

Here is an article on differences between absorption and emission spectra, which are higher order or semantic(language used, "as absorption has continuous spectra because the lines are a depletion of the continuum") differences.

The video is talking of the fact that in a real experiment, de-excitation of an atom can take multiple routes which cannot be available when shining light to get an absorption spectrum.

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