Is this really an excited state?

  • #1

Main Question or Discussion Point

The figure below is from a textbook. It is explaining what excited states are using carbon as an example. I don't necessarily agree that the the state labeled as "example excited state 1" is really an excited state. Since the electrons in the 2p orbitals are unpaired, and in the absence of a magnetic field spin up and spin down electrons have the same energy, I think this state has the same energy as the ground state.

My understanding of the Hund's rule is that electrons in degenerate energy orbitals are accommodated to maximize spin multiplicity, but again, these two states have the same spin multiplicity. Am I correct in my thinking that this is not really an excited state?

( Note in case the figure does not show correctly: The figure claims that an state with two unpaired electrons in the 2p orbitals for carbon is an excited state if the electrons have opposite spin. Each of these electrons is in a different 2p orbital. )

upload_2018-10-19_20-38-40.png
 

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  • #2
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My understanding of the Hund's rule is that electrons in degenerate energy orbitals are accommodated to maximize spin multiplicity
They are arranged that way because this state has the lowest energy - even without external magnetic field as the electrons interact with each other. The effect is not that strong, but it is there.
 
  • #3
DrDu
Science Advisor
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My understanding of the Hund's rule is that electrons in degenerate energy orbitals are accommodated to maximize spin multiplicity, but again, these two states have the same spin multiplicity.
No, they don't have the same spin multiplicity. The ground state is a triplet while the E1 state is a singlet.
The energetic difference between the two is also not due to magnetic effect but to the Pauli principle. In the triplet ground state, the Pauli principle forbids that the two electrons with like spins approach each other. This reduces their electrostatic repulsion. In the singlet state, the distance between the electrons will be smaller on average, resulting in a higher repulsion (and energy).
 

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