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Chem 355 10 Lecture 20 Electronic Absorption Spectroscopy

Chem 355 10 Lecture 20 Electronic Absorption Spectroscopy a) Hunds’ 3 rd rule and S-O coupling. Gold Medal Ranking Midterm Ranking Canada - - - - - - Barbados. Gold Medal Ranking Midterm Ranking Canada - - - - - - Barbados.

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Chem 355 10 Lecture 20 Electronic Absorption Spectroscopy

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  1. Chem 355 10 Lecture 20 Electronic Absorption Spectroscopy a) Hunds’ 3rd rule and S-O coupling

  2. Gold Medal Ranking Midterm Ranking Canada - - - - - - Barbados

  3. Gold Medal Ranking Midterm Ranking Canada - - - - - - Barbados

  4. For 2 equivalent p-electrons the microstates consistent with the Pauli Exclusion Principle resulted in 3 possible states with differing energies:

  5. For 2 equivalent p-electrons the microstates consistent with the Pauli Exclusion Principle resulted in 3 possible states with differing energies: These would represent the possible states for e.g. a C-or O-atom.

  6. For 2 equivalent p-electrons the microstates consistent with the Pauli Exclusion Principle resulted in 3 possible states with differing energies: These would represent the possible states for e.g. a C-or O-atom. From Hund’s 1st rule, the state of lowest energy in either case is: Followed with increasing energy from Hund’s 2nd rule by:

  7. Applying Hund’s 3rd rule to the energies of the allowed state results in a difference between the C- and O-atoms. The possible J values in either case are J = 0, J = 2.

  8. Applying Hund’s 3rd rule to the energies of the allowed state results in a difference between the C- and O-atoms. The possible J values in either case are J = 0, J = 2. In the C-atom in which the p-shell is less than half filled, the J = 0 state is lowest in energy, while in the O-atom in which the p-shell is more than half filled, it is the J = 2 state that is lowest in energy.

  9. Applying Hund’s 3rd rule to the energies of the allowed state results in a difference between the C- and O-atoms. The possible J values in either case are J = 0, J = 2. In the C-atom in which the p-shell is less than half filled, the J = 0 state is lowest in energy, while in the O-atom in which the p-shell is more than half filled, it is the J = 2 state that is lowest in energy. This difference in energy level based on J is the result of coupling between the magnetic moments associated with the spin and orbital angular momentum, or spin-orbit coupling.

  10. The energy level diagram for the sodium D lines 16 973 16 956 17 cm-1 589.8 nm 589.2 nm

  11. Selection Rules: The transitions between the electronic states in atoms is governed by the selection rules: Dn is unrestricted D = ± 1 Ds = 0 A fine structure selection rule is: DJ = 0, ± 1 except JJ The selection rules apply equally to absorption and emission. With atomic transition, in particular, most of the transition have been observed in emission from higher states populated in flames or plasma.

  12. Selection Rules: The transitions between the electronic states in atoms is governed by the selection rules: Dn is unrestricted D = ± 1 Ds = 0 A fine structure selection rule is: DJ = 0, ± 1 except JJ The selection rules apply equally to absorption and emission. With atomic transition, in particular, most of the transition have been observed in emission from higher states populated in flames or plasma.

  13. Selection Rules: The transitions between the electronic states in atoms is governed by the selection rules: Dn is unrestricted D = ± 1 Ds = 0 A fine structure selection rule is: DJ = 0, ± 1 except JJ The selection rules apply equally to absorption and emission. With atomic transition, in particular, most of the transition have been observed in emission from higher states populated in flames or plasma.

  14. Selection Rules: The transitions between the electronic states in atoms is governed by the selection rules: Dn is unrestricted D = ± 1 Ds = 0 A fine structure selection rule is: DJ = 0, ± 1 except JJ The selection rules apply equally to absorption and emission. With atomic transition, in particular, most of the transition have been observed in emission from higher states populated in flames or plasma.

  15. Selection Rules: The transitions between the electronic states in atoms is governed by the selection rules: Dn is unrestricted D = ± 1 Ds = 0 A fine structure selection rule is: DJ = 0, ± 1 except JJ The selection rules apply equally to absorption and emission. With atomic transition, in particular, most of the transition have been observed in emission from higher states populated in flames or plasma.

  16. Selection Rules: The transitions between the electronic states in atoms is governed by the selection rules: Dn is unrestricted D = ± 1 Ds = 0 A fine structure selection rule is: DJ = 0, ± 1 except JJ The selection rules apply equally to absorption and emission. With atomic transition, in particular, most of the transition have been observed in emission from higher states populated in flames or plasma.

  17. The nature of the Sodium D lines 3p ml = 0 s= 1/2 3s

  18. 3p 3s

  19. ml = 1, s= 1/2, J = 3/2 3p 3s

  20. 3p 3s

  21. 3p ml = 1, s= 1/2, J = 1/2 3s

  22. 3p ≈ 16,960 cm-1 (16,956; 16,973) 3s ≈ 589.6 nm =16,960 cm-1x 2.998 x1010 cms-1 = 5.08x1014 s-1

  23. 3p ≈ 16,960 cm-1 (16,956; 16,973) 3s ≈ 589.6 nm =16,960 cm-1x 2.998 x1010 cms-1 = 5.08x1014 s-1

  24. The energy level diagram for the sodium D lines 16 973 16 956 17 cm-1 589.8 nm 589.2 nm

  25. The levels of a 2P term arises from spin-orbit coupling due to the single p-electron. The low-j level lies below the high- j level. Energy j = 3/2 +1/2hcA 2p1 j = 1/2 –hcA This dependence of the splitting above arises from the spin-orbit coupling referred to above. The splittings above can be derived from: El,s,j= 1/2hcA{(j(j+1) – l(l+1) – s(s+1)} With l =1, s = 1/2 and j = 3/2 or 3/2; A = the spin-orbit coupling constant (specific for a particular atom)

  26. The levels of a 2P term arises from spin-orbit coupling due to the single p-electron. The low-j level lies below the high- j level. Energy j = 3/2 +1/2hcA 2p1 j = 1/2 –hcA This dependence of the splitting above arises from the spin-orbit coupling referred to above. The splittings above can be derived from: El,s,j= 1/2hcA{(j(j+1) – l(l+1) – s(s+1)} With l =1, s = 1/2 and j = 3/2 or 3/2; A = the spin-orbit coupling constant (specific for a particular atom)

  27. The levels of a 2P term arises from spin-orbit coupling due to the single p-electron. The low-j level lies below the high- j level. Energy j = 3/2 +1/2hcA 2p1 j = 1/2 –hcA This dependence of the splitting above arises from the spin-orbit coupling referred to above. The splittings above can be derived from: El,s,j= 1/2hcA{(j(j+1) – l(l+1) – s(s+1)} With l =1, s = 1/2 and j = 1/2 or 3/2; A = the spin-orbit coupling constant (specific for a particular atom)

  28. The spin-orbit coupling expression on the previous slide i.e. for a single electron can be derived from the interaction of a dipole (magnetic) in a field: The magnetic moment can be s and the B-field dependent on l, or vice versa. The term can be shown to be a function s, l and j from the following: The square of the magnitude of an angular momentum vector is proportional to: j(j+1), l(l+1), and j(j+1) where j, l and s are the corresponding quantum numbers.

  29. The spin-orbit coupling expression on the previous slide i.e. for a single electron can be derived from the interaction of a dipole (magnetic) in a field: The magnetic moment can be s and the B-field dependent on l, or vice versa. The term can be shown to be a function s, l and j from the following: The square of the magnitude of an angular momentum vector is proportional to: j(j+1), l(l+1), and j(j+1) where j, l and s are the corresponding quantum numbers.

  30. The spin-orbit coupling expression on the previous slide i.e. for a single electron can be derived from the interaction of a dipole (magnetic) in a field: The magnetic moment can be s and the B-field dependent on l, or vice versa. The term can be shown to be a function s, l and j from the following: The square of the magnitude of an angular momentum vector is proportional to: j(j+1), l(l+1), and j(j+1) where j, l and s are the corresponding quantum numbers.

  31. The spin-orbit coupling expression on the previous slide i.e. for a single electron can be derived from the interaction of a dipole (magnetic) in a field: The magnetic moment can be s and the B-field dependent on l, or vice versa. The term can be shown to be a function s, l and j from the following: The square of the magnitude of an angular momentum vector is proportional to: j(j+1), l(l+1), and s(s+1) where j, l and s are the corresponding quantum numbers.

  32. The last expression can be expressed as: It then follows that the interaction energy is given by:

  33. The last expression can be expressed as: It then follows that the interaction energy is given by:

  34. The last expression can be expressed as: It then follows that the interaction energy is given by:

  35. Spin-orbit coupling The lower energy associated with the more than half-filled subshells or larger J is associated with the fact that “spin-orbit coupling” is proportional to the total angular momentum in the atom mspin morbit morbit stronger coupling weak coupling The total angular momentum is large when the spin and orbital angular momentum vectors, and therefore the magnetic moments are in the same direction.

  36. Spin-orbit coupling The lower energy associated with the more than half-filled subshells or larger J is associated with the fact that “spin-orbit coupling” is proportional to the total angular momentum in the atom mspin morbit morbit stronger coupling weak coupling The total angular momentum is large when the spin and orbital angular momentum vectors, and therefore the magnetic moments are in the same direction.

  37. The L+ S states lie slightly lower in energy than the L– S states.

  38. The L+ S states lie slightly lower in energy than the L– S states. Spin-orbit (S-O) coupling is proportional to the nuclear charge and therefore becomes increasingly significant in larger atoms. This aspect of S-O coupling is not immediately evident based on the interaction of an electron with itself.

  39. The L+ S states lie slightly lower in energy than the L– S states. Spin-orbit (S-O) coupling is proportional to the nuclear charge and therefore becomes increasingly significant in larger atoms. This aspect of S-O coupling is not immediately evident based on the interaction of an electron with itself. However, if the interaction is thought of in terms of the relative motion of the nucleus with respect to the electron, the interaction then becomes a function of Z2

  40. morbit(Ze) mspin In the figure above the nucleus with a nuclear change Z is viewed as orbiting the electron. The vector due to the nuclear orbital motion is directly at the electron.

  41. morbit(Ze) mspin In the figure above the nucleus with a nuclear change Z is viewed as orbiting the electron. The vector due to the nuclear orbital motion is directly at the electron. The accepted theoretical treatment of spin-orbit coupling relates the interaction to the gradient of the potential near the nucleus where the electron is not shielded by the other electrons. The high velocity of the electron is proportional Z2 and the overall interaction proportional to Z4.

  42. Spin-orbit interaction and its dependence on nuclear charge appears directly in the absorption and emission spectra of e.g. alkali metals, and has pronounced effects on the excited-state processes in molecules and atoms. S-O interactions are particularly significant in influencing radiative and non-radiative spin-forbidden transition.

  43. “The strength of the spin-orbit coupling depends on the nuclear charge. To understand why this is so, imagine riding on the orbiting electron and seeing a charged nucleus apparently orbiting around us (like the Sun rising and setting).

  44. “The strength of the spin-orbit coupling depends on the nuclear charge. To understand why this is so, imagine riding on the orbiting electron and seeing a charged nucleus apparently orbiting around us (like the Sun rising and setting). As a result, we find ourselves at the centre of a ring of current. The greater the nuclear-charge the greater this current, and therefore the stronger the magnetic field we detect.

  45. “The strength of the spin-orbit coupling depends on the nuclear charge. To understand why this is so, imagine riding on the orbiting electron and seeing a charged nucleus apparently orbiting around us (like the Sun rising and setting). As a result, we find ourselves at the centre of a ring of current. The greater the nuclear-charge the greater this current, and therefore the stronger the magnetic field we detect. Because the spin magnetic moment of the electron interacts with this orbital magnetic field, it follows that, the greater the nuclear charge, the stronger the spin-orbit coupling. The coupling increases sharply with atomic number (as Z4).” From: Physical Chemistry, 7ed: P. Atkins & J. de Paula

  46. The familiar Na D-line splitting is observed to increase significantly with nuclear charge within the alkaline metal series. Li: 0.23 cm-1, Na:17 cm-1, K:38.5 cm-1, Cs:370 cm-1

  47. End of Lecture 20

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