Question

Which is correct among the following statements? (1) Radius of Cl atom is \(0.99 \AA\) while that of \(\mathrm{Cl}^{4}\) ion is \(1.54 \AA\). (2) Radius of \(\mathrm{Cl}\) atom is \(0.99 \mathrm{~A}\) while that of \(\mathrm{Na}\) atom is \(1.54 \mathrm{~A}\). (3) Radius of Cl atom is \(0.95 \Lambda\) while that of \(\mathrm{Cl}^{-}\) ion is \(0.81 \AA\). (4) Radius of Na atom is \(0.95 \AA\) while that of \(\mathrm{Na}\) ' ion is \(1.54 \Lambda\).

Short answer

Statement (2) is correct.

Step-by-step solution

Analyze Statement (1)

Statement (1) claims that the radius of a Cl atom is \(0.99 \, \text{Å}\) and the radius of a \( \text{Cl}^{4-} \) ion is \(1.54 \, \text{Å} \). Note that \( \text{Cl}^{4-} \) is not a common ion and usually does not exist. Therefore, Statement (1) is incorrect.

Analyze Statement (2)

Statement (2) proposes that the radius of a Cl atom is \(0.99 \, \text{Å}\) and the radius of a Na atom is \(1.54 \, \text{Å}\). For neutral atoms, chlorine (Cl) has a smaller radius than sodium (Na). Thus, Statement (2) could be correct.

Analyze Statement (3)

Statement (3) claims the radius of a Cl atom is \(0.95 \, \text{Å} \) and the radius of a \( \text{Cl}^{-} \) ion is \(0.81 \, \text{Å} \). In reality, the radius of a \( \text{Cl}^{-} \) ion is actually larger than that of a neutral Cl atom because the addition of an electron causes electron-electron repulsion, thus increasing the size. Hence, Statement (3) is incorrect.

Analyze Statement (4)

Statement (4) claims that the radius of a Na atom is \(0.95 \, \text{Å} \) and the radius of a \( \text{Na}^{+} \) ion is \(1.54 \, \text{Å} \). In reality, the radius of \( \text{Na}^{+} \) ion is smaller than the neutral Na atom because losing an electron reduces repulsion among the electrons. Therefore, Statement (4) is incorrect.

Conclusion

Compare all the given statements and verify with known data: Statements (1), (3), and (4) are incorrect based on atomic and ionic radii properties. Thus, Statement (2) is correct.

Key concepts

Radius of Chlorine Atom

Understanding the size of an atom, referred to as its atomic radius, is a fundamental concept in chemistry. For chlorine (Cl), the atomic radius is approximately 0.99 Å (angstroms). This value is an average distance from the nucleus of the chlorine atom to the outermost electron orbital.
Several factors affect the atomic radius, including the number of protons in the nucleus, the number of electron shells, and the effective nuclear charge. For chlorine, which sits in Group 17 of the periodic table, its atomic radius is smaller compared to elements in the same period but in different groups due to higher effective nuclear charge pulling the outer electrons closer to the nucleus.
Understanding this concept helps students grasp why chlorine has the specific radius it has and how it compares to other elements. The atomic radius is crucial for predicting and explaining many chemical properties and behaviors, such as atomic bonding and reactivity.

Radius of Sodium Atom

When examining the sodium atom (Na), it has a significantly larger atomic radius compared to chlorine, measuring around 1.54 Å. Sodium is located in Group 1 of the periodic table and has only one electron in its outermost shell.
This outer electron is less tightly bound due to the lower effective nuclear charge experienced by the electron, resulting in a larger atomic radius. Additionally, sodium has fewer protons than chlorine, decreasing the pull on the outermost electrons and thereby making the atom larger. Understanding these factors clarifies why sodium, despite being next to chlorine in the periodic table, has a much larger atomic radius. These differences in atomic radii also play an essential role in their chemical reactivity and the types of compounds they can form.

Ion Sizes and Electron Repulsion

The size of an ion compared to its parent atom changes due to the gain or loss of electrons. When an atom becomes negatively charged, gaining an electron (like Cl becoming Cl⁻), the ionic radius increases. This increase is due to electron-electron repulsion in the added electron shell, expanding the overall size of the ion. For example, the radius of a Cl⁻ ion is larger than a neutral Cl atom.
Conversely, when an atom loses an electron and becomes positively charged (like Na to Na⁺), the ionic radius decreases. The loss of an electron reduces the number of electron-electron repulsions, allowing the remaining electrons to be pulled closer to the nucleus. Consequently, a Na⁺ ion is smaller than a neutral Na atom. This understanding helps explain the variations seen in ion sizes compared to their atomic counterparts and is key for understanding the changes in physical properties such as solubility, melting points, and electrical conductivity when elements form ions.

Atomic and Ionic Radii Comparison

Comparing atomic and ionic radii provides essential insights into the behavior and reactivity of elements. For instance, chlorine has an atomic radius of about 0.99 Å, but as an ion, Cl⁻ has a larger radius due to increased electron-electron repulsion. On the other hand, sodium has an atomic radius of approximately 1.54 Å, which diminishes when it becomes a Na⁺ ion due to electron loss and reduced repulsion.
Solely considering the atomic radius, sodium is larger than chlorine. However, these trends reverse when comparing their ionic forms. This comparison highlights how the electron configuration and effective nuclear charge drastically alter the radii.

• Cl: 0.99 Å
• Cl⁻: larger than 0.99 Å
• Na: 1.54 Å
• Na⁺: smaller than 1.54 Å

These variations are crucial for predicting interaction properties, compound formations, and explaining chemical reactions. Understanding the comparison of atomic and ionic radii aids students in visualizing different elements' structural frameworks and their reactivities.