Given below are two statements :

Statement I : The metallic radius of $\mathrm{Na}$ is $1.86 \mathrm{~A}^{\circ}$ and the ionic radius of $\mathrm{Na}^{+}$ is lesser than $1.86 \mathrm{~A}^{\circ}$

Statement II : Ions are always smaller in size than the corresponding elements.

In the light of the above statements, choose the correct answer from the options given below :

<p>To determine the correctness of the given statements, let's analyze each one individually based on atomic and ionic radii concepts.</p> <hr /> <h3><strong>Statement I:</strong></h3> <p><strong>The metallic radius of $\mathrm{Na}$ is $1.86\, \text{Å}$ and the ionic radius of $\mathrm{Na}^+$ is lesser than $1.86\, \text{Å}$.</strong></p> <p><strong>Analysis:</strong></p> <p><p><strong>Metallic Radius of Sodium ($\mathrm{Na}$):</strong></p></p> <p><p>Sodium is a metal, and its metallic radius is indeed approximately $1.86\, \text{Å}$.</p></p> <p><p>The metallic radius refers to half the distance between the nuclei of two adjacent atoms in a metallic lattice.</p></p> <p><p><strong>Ionic Radius of Sodium Ion ($\mathrm{Na}^+$):</strong></p></p> <p><p>When sodium loses an electron to form $\mathrm{Na}^+$, it loses its outermost electron shell (the 3s orbital).</p></p> <p><p>This results in a significant decrease in size due to:</p> <p><p><strong>Decrease in Electron-Electron Repulsion:</strong> Fewer electrons mean less repulsion among them.</p></p> <p><p><strong>Unchanged Nuclear Charge:</strong> The number of protons remains the same, so the effective nuclear charge per electron increases, pulling the remaining electrons closer to the nucleus.</p></p></p> <p><p>The ionic radius of $\mathrm{Na}^+$ is approximately $0.95\, \text{Å}$, which is <strong>significantly smaller than $1.86\, \text{Å}$</strong>.</p></p> <p><strong>Conclusion:</strong></p> <p><strong>Statement I is correct.</strong></p> <hr /> <h3><strong>Statement II:</strong></h3> <p><strong>Ions are always smaller in size than the corresponding elements.</strong></p> <p><strong>Analysis:</strong></p> <p><p><strong>General Trends:</strong></p></p> <p><p><strong>Cations ($\text{Positive Ions}$):</strong></p> <p><p>Formed by the loss of one or more electrons.</p></p> <p><p><strong>Result:</strong> Cations are <strong>smaller</strong> than their parent atoms due to loss of electron(s) and decreased electron-electron repulsion.</p></p> <p><p><strong>Example:</strong> $\mathrm{Na} \rightarrow \mathrm{Na}^+$ (size decreases).</p></p></p> <p><p><strong>Anions ($\text{Negative Ions}$):</strong></p> <p><p>Formed by the gain of one or more electrons.</p></p> <p><p><strong>Result:</strong> Anions are <strong>larger</strong> than their parent atoms due to added electron(s) and increased electron-electron repulsion.</p></p> <p><p><strong>Example:</strong> $\mathrm{Cl} \rightarrow \mathrm{Cl}^-$ (size increases).</p></p></p> <p><p><strong>Exceptions to Statement II:</strong></p></p> <p><p>Since anions are larger than their corresponding neutral atoms, the statement that <strong>"ions are always smaller in size than the corresponding elements"</strong> is <strong>incorrect</strong>.</p></p> <p><strong>Conclusion:</strong></p> <p><strong>Statement II is false.</strong></p> <hr /> <h3><strong>Final Answer:</strong></h3> <p><strong>Statement I is correct but Statement II is false.</strong></p>