Slater's Rules — Z_effJEE Advanced

Concept

Outer electrons don't feel the full nuclear charge — inner electrons shield it. Slater's recipe for the screening constant σ: same-group electrons contribute 0.35 each, (n−1)-shell 0.85, deeper shells 1.00 (for s/p targets). $Z_{eff} = Z - \sigma$ then explains atomic radii, ionisation energies and the entire shape of the periodic table.

Key formula

Derivation

Same-shell electrons are diffuse and screen poorly (0.35); the shell just below overlaps substantially (0.85); core shells sit almost entirely inside (1.00).

For a d/f target electron, EVERYTHING below counts 1.00 — d electrons are terrible at being shielded, which is why Z_eff jumps across the 3d row and causes the d-block contraction.

Scenarios to explore

• Slater's Rules — Z_eff = Z − σ — the shielding arithmetic behind all trends.

Real-world applications

• Trends: Z_eff rises across a period (radius shrinks, IE climbs).
• Why 4s fills before 3d but IONISES first (3d shields 4s poorly once occupied).
• Lanthanide contraction: f electrons shield worst of all.

JEE exam tips

• Across period 2: Z_eff on the outer electron goes ~1.3 (Li) → ~5.85 (F) — the whole trend story.
• Isoelectronic series: same σ, rising Z ⇒ rising Z_eff ⇒ shrinking radius (N³⁻ > O²⁻ > F⁻ > Na⁺).
• 1s pair: σ = 0.30 for the other 1s electron (special rule).

Common mistakes

• Counting the target electron itself in σ.
• Using 0.85 for ALL inner electrons (only the n−1 shell).
• Grouping s and p separately — Slater lumps (ns, np) as one group.

Exam traps to avoid

• Z_eff for a 3d electron in Zn ≈ 8.85 — much larger than for the 4s (≈4.35): d electrons are held tighter.
• Slater is an approximation — it can't resolve s/p differences within a shell.