The Multi-Proton Nucleus, Orbital Contraction, Effective Nuclear Charge & Slater’s Rules

Orbital Contraction

Decrease in the size of an atomic orbital due to an increase in effective nuclear charge (Z_eff)

Effective Nuclear Charge (Z_eff)

The net positive charge experienced by an electron after accounting for shielding by inner electrons; Z_eff = Z - S

Screening Effect

The ability of inner electrons to shield outer electrons from the nucleus's full positive charge

Multi-proton nucleus

A nucleus with more than one proton; any atom other than hydrogen

Effect of screening on Z_eff

Increased screening effect reduces Z_eff; less attraction between nucleus and outer electrons

Effect of Z_eff on orbital size

Higher Z_eff pulls electrons closer, causing orbital contraction

Trend of orbital contraction across a period

Z_eff increases → orbital contraction increases

Trend of orbital size down a group

Z_eff decreases slightly → atomic size increases

Symbol for screening constant

S

Equation for effective nuclear charge

Z_eff = Z - S, where Z is nuclear charge and S is the screening constant

Slater's Rules

Predicts Z_eff by assigning different screening values (S) to electrons based on position

Aufbau Principle

States that electrons fill orbitals starting from the lowest energy level to the highest

Slater's Rule: ns/np electrons in same group

Each contributes S = 0.35

Slater's Rule: (n-1) shell electrons

Each contributes S = 0.85

Slater's Rule: (n-2) or lower shell electrons

Each contributes S = 1.00

Slater's Rule: nd/nf electrons in same group

Each contributes S = 0.35

Slater's Rule: Lower group than nd/nf

Each contributes S = 1.00

Electron affinity

Energy change when an electron is added to a neutral atom; usually releases energy

Trend of electron affinity across a period

Generally increases (more negative) left to right

Ionization energy

Energy required to remove an electron from a gaseous atom or ion

Trend of ionization energy across a period

Increases left to right due to increased Z_eff

Trend of ionization energy down a group

Decreases due to increased atomic size and shielding

Why 4s fills before 3d

4s orbital experiences higher Z_eff than 3d; it's lower in energy in neutral atoms

Example: Z_eff for 4s in K

19 - [(0 x 0.35) + (8 x 0.85) + (10 x 1.00)] = 2.20

Example: Z_eff for 3d in K

19 - [(0 x 0.35) + (18 x 1.00)] = 1.00

Most stable configuration for potassium

1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ (more stable than 3d¹)