Atomic Radius: Types & Periodic Trends
The Atomic Radius is generally defined as the distance from the center of the nucleus to the outermost shell of electrons. However, since the electron cloud has no sharp boundary, the radius is defined operationally based on the chemical environment of the atom.
1. Types of Atomic Radius
Depending on the nature of bonding, atomic radius is classified into three main types:
A. Covalent Radius ($r_{cov}$)
It is one-half of the distance between the nuclei of two identical atoms bonded by a single covalent bond.
Used for non-metals (e.g., $Cl_2$, $H_2$).
B. Metallic Radius ($r_{met}$)
It is one-half of the internuclear distance between two adjacent metal atoms in a metallic crystal lattice.
Used for metals (e.g., Na, Cu). Metallic bonds are weaker/longer than covalent bonds.
C. Van der Waals Radius ($r_{vdw}$)
It is one-half of the distance between the nuclei of two non-bonded, isolated atoms (or adjacent atoms belonging to two neighboring molecules) in the solid state.
Used for Noble Gases and non-bonded molecules.
Comparison of Magnitude
$$ r_{vdw} > r_{met} > r_{cov} $$
Van der Waals forces are the weakest, so atoms are furthest apart. Covalent bonds involve orbital overlap, bringing atoms closest.
2. Ionic Radius
The effective distance from the center of the nucleus of an ion up to which it has an influence on its electron cloud.
Cationic Radius
Formed by loss of electrons.
Size: Cation < Neutral Atom
Reason: Effective nuclear charge ($Z_{eff}$) increases as electrons decrease while protons remain same.
Anionic Radius
Formed by gain of electrons.
Size: Anion > Neutral Atom
Reason: Increased electron-electron repulsion expands the electron cloud; $Z_{eff}$ decreases.
3. Isoelectronic Species
Atoms or ions having the same number of electrons (e.g., $N^{3-}, O^{2-}, F^-, Na^+, Mg^{2+}, Al^{3+}$ all have 10 electrons).
$$ Al^{3+} < Mg^{2+} < Na^+ < F^- < O^{2-} < N^{3-} $$
4. Periodic Trends
A. Across a Period (Left to Right)
Trend: Atomic Radius Decreases.
Reason: Electrons enter the same shell. Nuclear charge increases, increasing the attraction ($Z_{eff}$) on valence electrons, pulling them closer.
Exception: Noble gases have the largest radius in their respective periods because we measure their Van der Waals radius (non-bonded), whereas others are measured as covalent/metallic radii.
B. Down a Group (Top to Bottom)
Trend: Atomic Radius Increases.
Reason: Number of shells ($n$) increases. The shielding effect of inner shells outweighs the increase in nuclear charge.
5. Important Anomalies
- Group 13 Anomaly ($Al \approx Ga$): The size of Gallium ($135 \ pm$) is smaller than or almost equal to Aluminum ($143 \ pm$). This is due to the Poor Shielding of 3d-electrons (Transition Contraction).
- Lanthanoid Contraction (Group 4 & 5): The size of Zirconium ($Zr$, 4d) is almost identical to Hafnium ($Hf$, 5d).
Reason: Poor shielding of 4f-electrons leads to a higher $Z_{eff}$, contracting the size of 5d elements.
6. Summary Table
| Feature | Variation | Reason |
|---|---|---|
| Period (L $\to$ R) | Decreases | Increase in $Z_{eff}$ |
| Group (Top $\to$ Bottom) | Increases | Addition of new shells |
| Cation | Smaller than atom | Loss of shell / High $Z_{eff}$ |
| Anion | Larger than atom | e-e repulsion / Low $Z_{eff}$ |
Atomic Radius Quiz
Test your concepts on Periodic Properties. 10 MCQs with explanations.
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