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Zeff = Z - sigma (effective nuclear charge = actual charge minus shielding). Zeff determines most periodic trends.

Slater's rules for sigma: Same group (n,l) electrons → 0.35 each (0.30 for 1s). Inner shell (n-1) → 0.85 each $\frac{for s}{p electrons}$ or 1.00 $\frac{for d}{f}$. Deeper shells → 1.00 each.

Penetration order: s > p > d > f. s-electrons shield most effectively; f-electrons shield least (diffuse, poor penetration). This is why lanthanoid contraction occurs (4f electrons provide inadequate shielding).

Zeff increases across a period (Z increases by 1, sigma increases by less than 1). This drives the decrease in atomic radius and increase in IE.

Example calculation: Nitrogen (Z=7), 1$s^2$ 2$s^2$ 2$p^3$. For a 2p electron: same group = 4 x 0.35 = 1.40; 1s group = 2 x 0.85 = 1.70. Sigma = 3.10. Zeff = 7 - 3.10 = 3.90.