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The effective nuclear charge for a valence electron in Co²⁺ using Slater's rules is 20.10. Here's how to calculate it:
1. Electronic Configuration: Co²⁺ has the electronic configuration [Ar]3d⁷. Since we are interested in a valence electron, we focus on the 3d electrons.
2. Slater's Rules:
Group A (3d electrons): Each 3d electron contributes 0.35 to the shielding constant (S) except for the one we are interested in (it doesn't shield itself).
Group B (3s and 3p electrons): These electrons contribute 0.85 to S.
Group C (electrons in lower shells): These contribute 1.00 to S.
3. Calculation:
S = (7 - 1)
0.35 + 2
0.85 + 18
1.00 = 20.10
4. Effective Nuclear Charge (Zeff): Zeff = Z - S, where Z is the atomic number of cobalt (27).
Zeff = 27 - 20.10 = 6.90
Therefore, the effective nuclear charge for a valence electron in Co²⁺ is 6.90, but none of the provided options match this result. It seems there might be an error in the options provided.