Effective Nuclear Charge & Slater's Rules

CompleteFundamentals of Chemistry

Z* is the net nuclear charge felt by an electron after shielding by inner electrons. Slater's rules estimate it.

Full notes

Definition: Effective nuclear charge Z* = Z − σ, where Z is the atomic number and σ is the screening (shielding) constant due to inner electrons.

1. Screening effect

Inner electrons lie between the nucleus and outer electrons, reducing the pull felt by outer electrons. s > p > d > f shielding power for similar shells. Effective nuclear charge also explains electron-gain/ionization trends across periods.

2. Slater's rules (method)

Write the configuration in (1s)(2s,2p)(3s,3p)(3d)(4s,4p)(4d)(4f)... groups.
Electrons to the right of the group contribute 0.
Same-group electrons: 0.35 each (0.30 for 1s).
For ns,np electrons: (n−1) shell contributes 0.85 each; inner shells 1.00 each.
For nd,nf electrons: all lower groups contribute 1.00 each.
σ = sum; Z* = Z − σ.

Example: For Fluorine (1s² 2s² 2p⁵, Z=9): shielding for a 2p electron = 7×0.35 + 2×0.85 = 4.15. So Z* = 9 − 4.15 = 4.85.

Note: Exam point: a Slater calculation in a numerical question is common — show the group segmentation clearly.

Exam notes

Z* = Z − σ. s>p shell shielding. Slater's rule groupings (1s)(2s2p)(3s3p)(3d)(4s4p)... and the 0.35/0.85/1.00 contributions.

Important points

Z* explains smaller atomic radii, higher IE and higher EN across a period.

Common mistakes

Including electrons of higher groups in σ — they contribute zero.

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