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In this video, Sal Khan says that an electron reaches a higher energy state if the electron possesses more energy. So I assume that, say in the case of carbon, the electrons not in the S1 orbital have more energy. Where does this energy come from?

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In simple terms: The further apart the negatively charged electrons are from the positively charged nucleus, the higher is the potential energy of said electrons. When increasing the quantum number $n$, you automatically get further away from the nucleus. That is why the $2s$ electrons have a higher energy than $1s$ electrons. (That, and adding that the $1s$ electrons shield some of the nuclear charge.)

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