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Atomic Structure and Atomic Spectra

Atomic Structure and Atomic Spectra. Chapter 10. Spectra of complex atoms. Energy levels not solely given by energies of orbitals Electrons interact and make contributions to E Singlet and triplet states Spin-orbit coupling. Fig 10.18 Vector model for paired-spin electrons.

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Atomic Structure and Atomic Spectra

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  1. Atomic Structure and Atomic Spectra Chapter 10

  2. Spectra of complex atoms • Energy levels not solely given by energies of orbitals • Electrons interact and make contributions to E • Singlet and triplet states • Spin-orbit coupling

  3. Fig 10.18 Vector model for paired-spin electrons Multiplicity = (2S + 1) = (2·0 + 1) = 1 Singlet state Spins are perfectly antiparallel Ground state Excited state

  4. Fig 10.24 Vector model for parallel-spin electrons Three ways to obtain nonzero spin Multiplicity = (2S + 1) = (2·1 + 1) = 3 Triplet state Spins are partially parallel

  5. Fig 10.25 Grotrian diagram for helium Singlet – triplet transitions are forbidden

  6. Fig 10.26 Orbital and spin angular momenta Spin-orbit coupling Magnetogyric ratio

  7. Fig 10.27(a) Parallel magnetic momenta Total angular momentum (j) = orbital (l) + spin (s) e.g., for l = 0 → j = ½ for l = 1 → j = 3/2

  8. Fig 10.27(b) Opposed magnetic momenta

  9. Fig 10.27 Parallel and opposed magnetic momenta Total angular momentum (j) = orbital (l) + spin (s) e.g., for l = 0 → j = ½ for l = 1 → j = 3/2, ½ Result: For l > 0, spin-orbit coupling splits a configuration into levels

  10. Fig 10.28 Spin-orbit coupling of a d-electron (l = 2) j = l + 1/2 j = l - 1/2

  11. Energy levels due to spin-orbit coupling • Strength of spin-orbit coupling depends on • relative orientations of spin and orbital • angular momenta (= total angular momentum) • Total angular momentum described in terms of • quantum number j • Energy of level with QNs: s, l, and j • where A is the spin-orbit coupling constant El,s,j = ½ hcA{ j(j+1) – l (l+1) – s(s+1) }

  12. Fig 10.29 Levels of a 2P term arising from spin-orbit coupling of a 2p electron El,s,j = 1/2hcA{ j(j+1) – l(l+1) – s(s+1) } = 1/2hcA{ 3/2(5/2) – 1(2) – ½(3/2) = 1/2hcA and = 1/2hcA{ 1/2(3/2) – 1(2) – ½(3/2) = -hcA

  13. Fig 10.30 Energy level diagram for sodium D lines Fine structure of the spectrum

  14. Fig 10.31 Types of interaction for splitting E-levels In light atoms: magnetic Interactions are small In heavy atoms: magnetic interactions may dominate the electrostatic interactions

  15. Fig 10.32 Total orbital angular momentum (L) of a p and a d electron (p1d1 configuration) L = l1 + l2, l1 + l2 – 1,..., |l1 + l2| = 3, 2, 1 F D P

  16. Fig 10.33 Multiplicity (2S+1) of two electrons each with spin angular momentum = 1/2 S = s1 + s2, s1 + s2 – 1,..., |s1 - s2| = 1, 0 Triplet Singlet

  17. For several electrons outside the closed shell, • must consider coupling of all spin and all orbital • angular momenta • In lights atoms, use Russell-Saunders coupling • In heavy atoms, use jj-coupling

  18. Fig 10.34 Correlation diagram for some states of a two electron system Russell-Saunders coupling for atoms with low Z, ∴ spin-orbit coupling is weak: J = L+S, L+S-1,..., |L-S| jj-coupling for atoms with high Z, ∴ spin-orbit coupling is strong: J = j1 + j2

  19. Selection rules for atomic (electronic) transitions • Transition can be specified using term symbols • e.g., The 3p1→ 3s1 transitions giving the • Na doublet are: • 2P3/2→ 2S1/2 and 2P1/2→ 2S1/2 • In absorption: 2P3/2← 2S1/2 and 2P1/2← 2S1/2 • Selection rules arise from conservation of angular • momentum and photon spin of 1 (boson)

  20. Selection rules for atomic (electronic) transitions ΔS = 0 Light does not affect spin directly Δl = ±1 Orbital angular momentum must change ΔL = 0, ±1 Overall change in orbital angular momentum depends on coupling ΔJ = 0, ±1 Total angular momentum may or may or may not change: J = L + S

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