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Identify the ground state free ion term symbols and the ground state energy terms in both, octahedral and tetrahedral fields of Cu^2+. show working
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Cu^2+ Electronic Configuration and Term Symbols
Cu^2+ has the electronic configuration [Ar] 3d^9. We'll determine the ground state term symbols for both octahedral and tetrahedral fields by considering Hund's rules:
1. Maximum Multiplicity: The ground state has the maximum spin multiplicity (2S+1). In this case, we have 9 d electrons, so 5 are spin up, and 4 are spin down, leading to S = 1/2. Therefore, 2S+1 = 2.
2. Maximum L: The ground state has the maximum total orbital angular momentum (L). For d^9, L = 2 (from the sum of the individual ml values for the 9 electrons). This corresponds to a D term.
3. Lowest J (for less than half-filled shells): For less than half-filled d shells, the ground state has the lowest possible total angular momentum (J), which is calculated as J = |L - S|. In this case, J = |2 - 1/2| = 3/2.
Therefore, the ground state term symbol for a free Cu^2+ ion is ^2D3/2.
Octahedral Field
In an octahedral field, the d orbitals split into two levels: the lower energy t2g set (dxy, dyz, dzx) and the higher energy eg set (dx2-y2, dz2). Since Cu^2+ has 9 d electrons, the t2g level will be fully filled (6 electrons) and the eg level will have 3 electrons. This results in a single unpaired electron in the eg set, giving a spin multiplicity of 2S+1 = 2 and an L value of 0 (since all the electrons in the eg level have their spin paired). Therefore, the ground state term symbol for Cu^2+ in an octahedral field is ^2E. The energy term is ^2Eg.
Tetrahedral Field
In a tetrahedral field, the d orbital splitting is reversed compared to the octahedral field. The eg level is now lower in energy than the t2g level. Cu^2+ will have 6 electrons in the eg level and 3 in the t2g level. This gives us a spin multiplicity of 2S+1 = 2 and an L value of 1 (since there are unpaired electrons in the t2g level). Therefore, the ground state term symbol for Cu^2+ in a tetrahedral field is ^2T2. The energy term is ^2T2g.
Cu^2+ has the electronic configuration [Ar] 3d^9. We'll determine the ground state term symbols for both octahedral and tetrahedral fields by considering Hund's rules:
1. Maximum Multiplicity: The ground state has the maximum spin multiplicity (2S+1). In this case, we have 9 d electrons, so 5 are spin up, and 4 are spin down, leading to S = 1/2. Therefore, 2S+1 = 2.
2. Maximum L: The ground state has the maximum total orbital angular momentum (L). For d^9, L = 2 (from the sum of the individual ml values for the 9 electrons). This corresponds to a D term.
3. Lowest J (for less than half-filled shells): For less than half-filled d shells, the ground state has the lowest possible total angular momentum (J), which is calculated as J = |L - S|. In this case, J = |2 - 1/2| = 3/2.
Therefore, the ground state term symbol for a free Cu^2+ ion is ^2D3/2.
Octahedral Field
In an octahedral field, the d orbitals split into two levels: the lower energy t2g set (dxy, dyz, dzx) and the higher energy eg set (dx2-y2, dz2). Since Cu^2+ has 9 d electrons, the t2g level will be fully filled (6 electrons) and the eg level will have 3 electrons. This results in a single unpaired electron in the eg set, giving a spin multiplicity of 2S+1 = 2 and an L value of 0 (since all the electrons in the eg level have their spin paired). Therefore, the ground state term symbol for Cu^2+ in an octahedral field is ^2E. The energy term is ^2Eg.
Tetrahedral Field
In a tetrahedral field, the d orbital splitting is reversed compared to the octahedral field. The eg level is now lower in energy than the t2g level. Cu^2+ will have 6 electrons in the eg level and 3 in the t2g level. This gives us a spin multiplicity of 2S+1 = 2 and an L value of 1 (since there are unpaired electrons in the t2g level). Therefore, the ground state term symbol for Cu^2+ in a tetrahedral field is ^2T2. The energy term is ^2T2g.
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