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Chem 355 10 Lecture 19 Electronic Absorption Spectroscopy a) atomic states and microstates

Chem 355 10 Lecture 19 Electronic Absorption Spectroscopy a) atomic states and microstates . Hund’s Rules 1. The term with maximum multiplicity lies lowest in energy 2. For a given multiplicity, the term with the largest value of L lies lowest in energy.

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Chem 355 10 Lecture 19 Electronic Absorption Spectroscopy a) atomic states and microstates

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  1. Chem 355 10 Lecture 19 Electronic Absorption Spectroscopy a) atomic states and microstates

  2. Hund’s Rules • 1. The term with maximum multiplicity lies lowest in energy • 2. For a given multiplicity, the term with the largest value of L lies lowest in energy. • For atoms with half-, or less than half-filled shells, the level with the lowest J lies lowest in energy.

  3. Hund’s Rules • 1. The term with maximum multiplicity lies lowest in energy • 2. For a given multiplicity, the term with the largest value of L lies lowest in energy. • For atoms with half-, or less than half-filled shells, the level with the lowest J lies lowest in energy. • For atoms with more than half-filled shells, the level of highest J lies lowest in energy.

  4. Physical Basis for Hund’s Rules 1.Electrons with the same spin cannot be in the same orbital (Pauli Exclusion Principle). In different orbitals electron-electron repulsions are therefore reduced.

  5. Physical Basis for Hund’s Rules • 1.Electrons with the same spin cannot be in the same orbital (Pauli Exclusion Principle). In different orbitals electron-electron repulsions are therefore reduced. • With electrons orbiting in the same direction i.e. with maximum L, the meet each other less often, and therefore the repulsive energy is lower.

  6. Physical Basis for Hund’s Rules • 1.Electrons with the same spin cannot be in the same orbital (Pauli Exclusion Principle). In different orbitals electron-electron repulsions are therefore reduced. • With electrons orbiting in the same direction i.e. with maximum L, the meet each other less often, and therefore the repulsive energy is lower. • 3. The coupling between isolated spin and orbital angular momentum vectors (spin-orbit coupling) that are in opposite directions, results in a negative energy change.

  7. The spectroscopic term symbol for the ground electronic configuration of the N-atom (K2s22p3) is: a) 1S3/2 b) 1P2 c) 3S1/2 d) 2P3/2 e) 4S3/2

  8. The spectroscopic term symbol for the ground electronic configuration of the N-atom (K2s22p3) is: a) 1S3/2 b) 1P2 c) 3S1/2 d) 2P3/2 e) 4S3/2

  9. In the ground state S is maximized focusing on the 2p substates: S =

  10. In the ground state S is maximized focusing on the 2p substates: S = 2S + 1 =

  11. In the ground state S is maximized focusing on the 2p substates: S = 2S + 1 =

  12. In the ground state S is maximized focusing on the 2p substates: S = 2S + 1 = Given the spin multiplicity, maximize L:

  13. In the ground state S is maximized focusing on the 2p substates: S = 2S + 1 = Given the spin multiplicity, maximize L: L = = 0

  14. In the ground state S is maximized focusing on the 2p substates: S = 2S + 1 = Given the spin multiplicity, maximize L: L = = 0 Total angular momentum: J = L + S = 0 + The term symbol for the ground state is: 4S3/2

  15. The spectroscopic term symbol for the ground electronic configuration of the Fe(26) atom (KL3s23p64s23d6) is: a) 5S5 b) 5D4 c) 6S5/2 d) 3P5 e) 4F5

  16. The spectroscopic term symbol for the ground electronic configuration of the Fe(26) atom (KL3s23p64s23d6) is: a) 5S5 b) 5D4 c) 6S5/2 d) 3P5 e) 4F5

  17. The spectroscopic term symbol for the ground electronic configuration of the Fe(26) atom (KL3s23p64s23d6) is: a) 5S5 b) 5D4 c) 6S5/2 d) 3P5 e) 4F5

  18. The spectroscopic term symbol for the ground electronic configuration of the Fe(26) atom (KL3s23p64s23d6) is: a) 5S5 b) 5D4 c) 6S5/2 d) 3P5 e) 4F5

  19. The spectroscopic term symbol for the ground electronic configuration of the Fe(26) atom (KL3s23p64s23d6) is: a) 5S5 b) 5D4 c) 6S5/2 d) 3P5 e) 4F5

  20. The spectroscopic term symbol for the ground electronic configuration of the Fe(26) atom (KL3s23p64s23d6) is: a) 5S5 b) 5D4 c) 6S5/2 d) 3P5 e) 4F5

  21. The spectroscopic term symbol for the ground electronic configuration of the Fe(26) atom (KL3s23p64s23d6) is: a) 5S5 b) 5D4 c) 6S5/2 d) 3P5 e) 4F5

  22. In the ground state S is maximized focusing on the 3d substates: S = = 2; Given the spin multiplicity, maximize L: L = = 2 Total angular momentum: J = L + S = 2 + 2 = 4 The term symbol for the ground state is: 5D4

  23. In the ground state S is maximized focusing on the 3d substates: S = = 2; 2S+1 = 5 Given the spin multiplicity, maximize L: L = = 2 Total angular momentum: J = L + S = 2 + 2 = 4 The term symbol for the ground state is: 5D4

  24. In the ground state S is maximized focusing on the 3d substates: S = = 2; 2S+1 = 5 Given the spin multiplicity, maximize L: L = = 2 Total angular momentum: J = L + S = 2 + 2 = 4 The term symbol for the ground state is: 5D4

  25. In the ground state S is maximized focusing on the 3d substates: S = = 2; 2S+1 = 5 Given the spin multiplicity, maximize L: L = = 2 Total angular momentum: J = L + S = 2 + 2 = 4 The term symbol for the ground state is: 5D4

  26. In the ground state S is maximized focusing on the 3d substates: S = = 2; 2S+1 = 5 Given the spin multiplicity, maximize L: L = = 2 Total angular momentum: J = L + S = 2 + 2 = 4 The term symbol for the ground state is: 5D4

  27. In the ground state S is maximized focusing on the 3d substates: S = = 2; 2S+1 = 5 Given the spin multiplicity, maximize L: L = = 2 Total angular momentum: J = L + S = 2 + 2 = 4 The term symbol for the ground state is: 5D4

  28. C-atom: (less than half-filled subset of orbitals, e.g p-orbitals); 3P0 lowest J, lowest E. N-atom: 4S3/2 (half-filled subset of orbitals, e.g. p-orbitals, L = 0, J = S. O-atom: (more that half-filled subset of orbitals, e.g p-orbitals); 3P2 highest J, lowest E F-atom: (more that half-filled subset of orbitals, e.g p-orbitals); 2P3/2 highest J, lowest E

  29. C-atom: (less than half-filled subset of orbitals, e.g p-orbitals); 3P0 lowest J, lowest E. N-atom: 4S3/2 (half-filled subset of orbitals, e.g. p-orbitals, L = 0, J = S. O-atom: (more that half-filled subset of orbitals, e.g p-orbitals); 3P2 highest J, lowest E F-atom: (more that half-filled subset of orbitals, e.g p-orbitals); 2P3/2 highest J, lowest E

  30. C-atom: (less than half-filled subset of orbitals, e.g p-orbitals); 3P0 lowest J, lowest E. N-atom: 4S3/2 (half-filled subset of orbitals, e.g. p-orbitals, L = 0, J = S. O-atom: (more that half-filled subset of orbitals, e.g p-orbitals); 3P2 highest J, lowest E F-atom: (more that half-filled subset of orbitals, e.g p-orbitals); 2P3/2 highest J, lowest E

  31. Finding the most stable electronic state of an atom is straightforward using Hunds’ rules. To find all of the remaining possible states for a given electronic configuration is not as staightforward. It is easy to overestimate the # of possible states that can exist.

  32. Finding the most stable electronic state of an atom is straightforward using Hunds’ rules. To find all of the remaining possible states for a given electronic configuration is not as staightforward. It is easy to overestimate the # of possible states that can exist. Consider the case e.g. C-atom in which 2 equivalent 2p-electrons are involved. How many states, and what are the term symbols of the states that can exist.

  33. Finding the most stable electronic state of an atom is straightforward using Hunds’ rules. To find all of the remaining possible states for a given electronic configuration is not as staightforward. It is easy to overestimate the # of possible states that can exist. Consider the case e.g. C-atom in which 2 equivalent 2p-electrons are involved. How many states, and what are the term symbols of the states that can exist.

  34. Finding the most stable electronic state of an atom is straightforward using Hunds’ rules. To find all of the remaining possible states for a given electronic configuration is not as staightforward. It is easy to overestimate the # of possible states that can exist. Consider the case e.g. C-atom in which 2 equivalent 2p-electrons are involved. How many states, and what are the term symbols of the states that can exist. This is usually done by filling in a table of micro-states for, e.g. in this case, 2 electrons at the 2p-level.

  35. Finding the most stable electronic state of an atom is straightforward using Hunds’ rules. To find all of the remaining possible states for a given electronic configuration is not as staightforward. It is easy to overestimate the # of possible states that can exist. Consider the case e.g. C-atom in which 2 equivalent 2p-electrons are involved. How many states, and what are the term symbols of the states that can exist. This is usually done by filling in a table of micro-states for, e.g. in this case, 2 electrons at the 2p-level. A table is set up containing all the possible combinations of ML and MS:

  36. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml =1 ml = 0 ml = -1

  37. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml =1 ml = 0 ml = -1

  38. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) We are first going to add all the microstates in which MS = 0, i.e. the spins are paired, and therefore all in the central column. ml =1 ml = 0 ml = -1

  39. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml =1 ml = 0 ml = -1

  40. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml =1 ml = 0 ml = -1

  41. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml = 1, ml =1 ml = 0 ml = -1

  42. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml = 1, ml = 1, ml =1 ml = 0 ml = -1

  43. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml = 1, ml = 1, a ml =1 ml = 0 ml = -1

  44. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml = 1, b ml = 1, a ml =1 ml = 0 ml = -1

  45. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml =1 ml = 0 ml = -1

  46. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml =1 ml = 0 ml = -1

  47. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml =1 ml = 0 ml = -1

  48. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml =1 ml = 0 ml = -1

  49. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml =1 ml = 0 ml = -1

  50. ML MS 1 0 -1 2 1 0 -1 -2 (1,1) (1,0)(1,0) (1,0) (1,-1) (1,-1)(1,-1)(0,0) (1,-1) (0,-1) (0,-1)(0,-1) (0,-1) (-1,-1) ml =1 ml = 0 ml = -1

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