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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

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

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**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. • For atoms with half-, or less than half-filled shells, the level with the lowest J lies lowest in energy.**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.**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.**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.**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.**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**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**In the ground state S is maximized focusing on the 2p**substates: S =**In the ground state S is maximized focusing on the 2p**substates: S = 2S + 1 =**In the ground state S is maximized focusing on the 2p**substates: S = 2S + 1 =**In the ground state S is maximized focusing on the 2p**substates: S = 2S + 1 = Given the spin multiplicity, maximize L:**In the ground state S is maximized focusing on the 2p**substates: S = 2S + 1 = Given the spin multiplicity, maximize L: L = = 0**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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.**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.**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.**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.**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:**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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