Understanding Spectroscopic Term Symbols: Unraveling the Confusion

[Talita]

Terrm symbols are really letting me confused.

A spectroscopic term or term symbol is used to identify different arrangments of a given electronic configuration. For example, to carbon in ground state (1s² 2s² 2p²) there are a lot of different possible values for ml and ms, and term symbols can describe these differences, as well as the different energies of the possible microstates.

That’s where my confusion starts: if a term symbol groups microstates with the same energy, how is that possible that some microstates from different orbitais with different energies are described by the same term symbol?

For example, 1s² and 2s² have different energies, but they are represented by the same term symbol (singlet S). It just doesn’t make sense to me.

You can see graphically my doubt in slide 10: http://www.clt.astate.edu/sreeve/Multielectron%20Atoms.pdf

I’m sorry, perhaps I just let thing more confusing haha And I’m sorry if i made any english mistake! (:

 

[Khashishi]

The term symbols label the entire electron state (all electrons), not one electron. You shouldn't think of each electron as having some unique energy, but rather, the entire state (all the electrons in some arrangement) have a unique energy, and a different arrangement will have a different energy. You can't simply sum the energy of each electron together because electrons interact with each other.

Just saying "1s² 2s¹ 2p¹" (the electron configuration) does not give you enough information to identify the state of all electrons, so you need to also have the term symbol. The term symbol uses capital letters to indicate that these are the sum over all electrons. Unfortunately, the same letters being used makes things confusing.

For example, the total spin S of two electrons in the orbitals "1s¹ 2s¹" can be either be 0 or 1 because the spins of each electron can add or subtract. The total orbital angular momentum L is 0 since each electron has an orbital angular momentum of 0. The total angular momentum is 0 or 1 depending on S. So the two possible states are
1s¹ 2s^{1 1}S₀
1s¹ 2s^{1 3}S₁

Unfortunately, the poor historical notation makes this much harder to understand than necessary.

 

[Talita]

Sorry for my late reply, Khashishi.

I understand what you said, but my doubt has not been answered yet :/
I see that 1s² and 2s² have the same configuration, but they don't correspond to the same orbital. So, the energies that describe them should be different. If the energies are different, why they are described by the same term symbol, once term symbols describe different energies?

 

[DrDu]

There may well be states of different energy with the same term symbol. It remains however true that if states have the same energy then they also have the same term symbol. The converse is not true in general.

 

[Khashishi]

The electron configuration and term symbol together identify an energy state. Just the term symbol by itself is not enough to identify a state, since more than one state has the same term symbol.