Chemistry 362Spring 2013Dr. Jean M. StandardApril 22, 2013

Atomic Term Symbols and Energy Splitting

1. Atomic Term Symbols and the Sodium D-LineThe sodium D-line is responsible for the familiar orange glow of many street lights. The origin of the glow isemission of photons in the visible region of the electromagnetic spectrum from excited sodium atoms. The excitedatoms emit light and return to their ground electronic states.

The sodium D-line gets its name because there are really two closely-spaced emissions possible, or a "doublet", asshown in Figure 1. These transitions occur at wavelengths of 5890 and 5896 Å.

Na 3p1

E

λ=5890 Åλ=5896 Å

Na 3s1

Figure 1. Sodium atom atomic emissions that produce the so-called D-line.

The doublet observed in the sodium D-line transition involves the outer electron in the sodium atom whichundergoes a transition from an excited 1s22s22p63p1 configuration to the ground state 1s22s22p63s1 configuration.To see why this electronic transition corresponds to a doublet, the atomic term symbols for the different electronicconfigurations must be determined. In both cases, only the outer open shell need be considered.

Sodium Atom Ground State 3s1 Term SymbolSince the ground state of sodium only has one outer electron, the total orbital angular momentum quantum number Land total spin angular momentum quantum number S are identical to the orbital and spin angular momentumquantum numbers of the outer electron. Thus,

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S = s1 = 12 and

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L = 1 = 0.

The multiplicity 2S+1 is therefore 2 (a doublet) and the state corresponds to a

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2S state. Then, all that is needed is todetermine the total angular momentum quantum number J.

The total angular momentum quantum number J ranges from

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L − S to

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L + S . For the

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2S state, L=0 and

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S = 12

leads to

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J = 12 .

Therefore, the only possible term symbol for the sodium 3s1 ground state is

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2S1/ 2 .

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Sodium Atom Excited State 3p1 Term SymbolThe 3p1 excited state of sodium only has one outer electron, so the total orbital angular momentum quantum numberL and total spin angular momentum quantum number S are identical to the orbital and spin angular momentumquantum numbers of the outer electron. Thus,

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S = s1 = 12 and

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L = 1 = 1.

The multiplicity 2S+1 is therefore 2 (a doublet) and the state corresponds to a

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2P state. Then, all that is needed is todetermine the total angular momentum quantum number J.

The total angular momentum quantum number J ranges from

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L − S to

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L + S . For the

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2P state, L=1 and

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S = 12

leads to two possible values of J,

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J = 12 and

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J = 32 .

Therefore, there are two possible term symbols for the sodium 3p1 excited state:

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2P1/ 2 and

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2P3/ 2 . Spin-orbitcoupling leads to energy splitting between these two terms.

Energy Level DiagramThe term symbols determined for the ground and excited states of sodium can be used to label the transitionsresponsible for the sodium D-line emission, as shown in Figure 2.

Na 2P1/2

E

λ=5890 Åλ=5896 Å

Na 2S1/2

Na 2P3/2

Figure 2. Atomic term symbols for transitions involved in the sodium D-line.

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3. Another Example of Energy Splitting of Atomic TermsConsider an example of an atomic electron configuration 1s12p1. There are 12 ways of choosing the individualquantum numbers for the two electrons in this configuration. In the absence of electron-electron repulsions, all thesestates are degenerate.

The possible term symbols for the 1s12p1 configuration are 1P and 3P (not including the J value). Hund's first rulestates that terms with higher multiplicity will be lower in energy. Thus, including electron-electron repulsion, 3Pwill be lower in energy than 1P.

For the 1P term, the only possible value of J is 1; thus, the only term symbol for this state is 1P1. For the 3P term, thepossible values of J are 0, 1, and 2; this leads to term symbols 3P0, 3P1, and 3P2. The total degeneracy of the 1P and3P terms is 3, 1, 3, and 5, respectively, for a total of 12 (in agreement with the 12 sets of individual quantumnumbers discussed above).

The 3P0, 3P1, and 3P2 states are split in energy by a very small amount. This splitting is due to the coupling of spinangular momentum (S) with total orbital angular momentum (L). This spin-orbit coupling splits levels within thesame term (that is, the same values of L and S) that have different values of J.

Finally, if the atom is placed in a magnetic field, the levels with the same values of L, S, and J, but with differentvalues of MJ are split. All of the energy splittings for the 1s12p1 electron configuration are summarized in Figure3.

no elec-elec elec-elec spin-orbit magnetic repulsion repulsion coupling field

Figure 3. Energy splitting of atomic terms in the 1s12p1 configuration.