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The effective nuclear charge (Zeff) for a valence electron in Co²⁺ can be calculated using Slater's rules. Here's how:
1. Electron Configuration: The electronic configuration of Co²⁺ is [Ar] 3d⁷.
2. Slater's Rules:
Electrons in the same group (n): Subtract 0.35 from the nuclear charge (Z) for each electron in the same group (n) as the valence electron (except for the valence electron itself).
Electrons in the n-1 group: Subtract 0.85 from Z for each electron in the n-1 group.
Electrons in the n-2 and lower groups: Subtract 1.00 from Z for each electron in the n-2 and lower groups.
3. Applying Slater's Rules: We are interested in the 3d electrons in Co²⁺.
n = 3: There are 6 other 3d electrons, so subtract 6
0.35 = 2.10 from Z.
n-1 = 2: There are 8 electrons in the 2s and 2p orbitals, so subtract 8
0.85 = 6.80 from Z.
n-2 and lower: Subtract 10
1.00 = 10.00 from Z (for the 1s and 2s electrons in the [Ar] core).
4. Calculation: The nuclear charge of Co is 27. So, Zeff = 27 - 2.10 - 6.80 - 10.00 = 8.10.
Therefore, the effective nuclear charge for a valence electron in Co²⁺ is approximately 8.10.