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Slater's rules are used to calculate the effective nuclear charge (Zeff) experienced by an electron in an atom. The shielding constant (S) represents the reduction in nuclear charge due to the presence of other electrons. For d orbitals, the shielding constant is calculated based on the number of electrons in the same shell (n) and the shells below (n-1). Specifically, the following contributions are added:
Inner shell electrons (n-1): Each inner shell electron contributes 0.85 to S.
Electrons in the same shell (n) but lower than d orbital: Each electron in the s and p orbitals of the same shell contributes 0.35 to S.
Electrons in the same shell (n) but higher than d orbital: Each electron in the d and f orbitals of the same shell contributes 0.35 to S.
For example, to calculate the shielding constant for a 3d electron in a cobalt atom (Co, Z=27), we have:
1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁷
S = (2
0.85) + (8
0.35) + (6
0.35) = 5.85
Zeff = Z - S = 27 - 5.85 = 21.15