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Last hour: Angular momentum in multielectron atoms

Learn about quantum numbers, LS coupling, term symbols, microstate analysis for atomic term symbols, and more in multielectron atoms. Dive into angular momentum in atoms & construct term symbols. Explore the emission & absorption spectrum of sodium.

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Last hour: Angular momentum in multielectron atoms

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  1. Last hour: Angular momentum in multielectron atoms • Total orbital angular momentum: quantum numbers: L, ML • Total spin: quantum numbers: S, MS • Total angular momentum: quantum numbers: J = L+S, …. , |L-S| in steps of 1; MJ = -J, …, +J • Levels of the same L  terms L = 0, 1, 2, 3, 4 S, P, D, F, G • LS coupling: for small Z, neglect spin-orbit coupling  makes total orbital, total spin, total angular momentum conserved  L, S, J are “good quantum numbers”, can be used to label terms • All terms have different energies • Atomic term symbols: 2S+1LJ • Microstate analysis to construct allowed term symbols

  2. Microstate Analysis for Constructing Atomic Term Symbols Step 1: Write down all possible values for L and S according to the electron configuration. Step 2: Construct a microstate table, containing all possible combinations of ML and MS, and fill it with microstates that can produce these combinations. Step 3: Identify states that are excluded due to the Pauli principle, and strike them from the table. Step 4: To obtain the first term symbol, identify the highest ML in the table, and the highest MS that belongs to this ML. The highest ML value will determine L of the term, and the MS belonging to it determines S. Strike one microstate from the table for each ML/MS combination that is part of the term. Step 5: Repeat Step 4 with the new (reduced) table until no more microstates are left.

  3. John Robinson Pierce, American engineer and author. Coined the term "transistor”, wrote science fiction under the pseudonym “J.J. Coupling”

  4. Emission and Absorption Spectrum of Sodium

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