Understanding Ionic Radii Variation

Ionic radius is the measure of the size of an ion in an ionic crystal. It depends on two main factors: the effective nuclear charge (Z_eff) and the screening effect (also called shielding effect).

Key Concepts:

• Effective Nuclear Charge (Z_eff): The net positive charge experienced by an electron in an atom, accounting for shielding by other electrons. It is calculated as: $Z_{\text{eff}}=Z-\sigma$ where Z is the atomic number and σ is the shielding constant.
• Screening Effect: The reduction in the effective nuclear charge due to the repulsion between electrons. Inner electrons shield outer electrons from the full nuclear charge.

How Ionic Radii Vary:

Step 1: Effective nuclear charge (Z_eff) attracts electrons closer to the nucleus. A higher Z_eff means stronger attraction, pulling the electron cloud inward, thus decreasing the ionic radius.

Therefore, ionic radius is in inverse proportion to the effective nuclear charge.

Step 2: Screening effect reduces the pull of the nucleus on outer electrons. A greater screening effect means outer electrons experience less attraction, so the electron cloud expands, increasing the ionic radius.

Thus, ionic radius is in direct proportion to the screening effect.

Step 3: The options involving "square" of these factors are incorrect because the relationship is linear, not quadratic. Ionic radius depends directly on screening and inversely on Z_eff, not on their squares.

Final Answer: Ionic radii vary in inverse proportion to the effective nuclear charge and direct proportion to the screening effect. So, the first two options are correct.

Related Topics:

• Periodic Trends in Atomic and Ionic Sizes
• Shielding Effect and Slater's Rules
• Ionization Energy and Electron Affinity
• Formation of Cations and Anions

Important Formulae and Theory:

• Effective Nuclear Charge: $Z_{\text{eff}}=Z-\sigma$
• For isoelectronic ions, size decreases with increasing nuclear charge.
• Across a period, ionic radius decreases due to increasing Z_eff.
• Down a group, ionic radius increases due to addition of shells and increased shielding.