Problem 157 - A Complete Resource Book in Chemistry for JEE Main

Question

The set representing the correct order of ionic radius is: \(\quad\) (a) \(\mathrm{Na}^{+}>\mathrm{Li}^{+}>\mathrm{Mg}^{2+}>\mathrm{Be}^{2+}\) (b) \(\mathrm{Li}^{+}>\mathrm{Na}^{+}>\mathrm{Mg}^{2+}>\mathrm{Be}^{2+}\) (c) \(\mathrm{Mg}^{2+}>\mathrm{Be}^{2+}>\mathrm{Li}^{2+}>\mathrm{Na}^{+}\) (d) \(\mathrm{Li}^{+}>\mathrm{Be}^{2+}>\mathrm{Na}^{+}>\mathrm{Mg}^{2+}\)

Step-by-Step Solution

Answer

Option (a) \\( \mathrm{Na}^{+} > \mathrm{Li}^{+} > \mathrm{Mg}^{2+} > \mathrm{Be}^{2+} \\\ is correct.

Step 1: Understand the Context

Ionic radius refers to the measure of an atom's ion in a crystal lattice. It varies depending on the charge of the ion and the atom's position on the periodic table. Positive ions or cations are generally smaller than their parent atoms.

Step 2: Analyze Cations in Each Option

Examine each ion: - \( \text{Li}^+ \) and \( \text{Na}^+ \) are Group 1 ions, while \( \text{Mg}^{2+} \) and \( \text{Be}^{2+} \) are Group 2 ions.- Compare ions of the same column in the periodic table (group) based on their period (row). \( \text{Na}^+ \) is larger than \( \text{Li}^+ \) because it is in a lower period.

Step 3: Apply the Charge Impact

Higher charged cations are smaller due to stronger attraction to electrons by the nucleus. Compare by charge first: \( \text{Mg}^{2+} \) and \( \text{Be}^{2+} \) are smaller than \( \text{Li}^+ \) and \( \text{Na}^+ \) because of the +2 charge compared to +1.

Step 4: Establish a Correct Order Based on Combined Factors

Combining both charge and period position:- For Group 1 ions: \( \text{Na}^+ > \text{Li}^+ \)- For Group 2 ions: \( \text{Be}^{2+} > \text{Mg}^{2+} \) because Be has fewer electron shells than Mg and more effective nuclear charge.

Step 5: Identify Correct Answer

Integrate the above logic:- The correct order by increasing ionic size is \( \text{smallest} : \text{Mg}^{2+} < \text{Be}^{2+} < \text{Li}^+ < \text{Na}^+ \), which is option (a).

Key Concepts

Cations

Cations are atoms or molecules that have lost one or more electrons, resulting in a positive charge. This occurs because the number of protons in the nucleus remains the same, but the loss of electrons results in a deficiency of negative charge. The formation of cations is pivotal when discussing ionic radii. Typically, when an atom becomes a cation, its ionic radius decreases. This shrinkage is due to a decreased electron-electron repulsion within the atom, which allows the nucleus to pull the remaining electrons closer.

• Cations are crucial in forming ionic compounds, where they pair with anions (negatively charged ions).
• The charge of a cation often corresponds to its group number in the periodic table, particularly for main group elements.

Understanding the behavior of cations is essential, as it influences the properties of the compounds they form.

Periodic Table

The periodic table is an organized chart of elements arranged by increasing atomic number and recurring chemical properties. This organization helps predict the characteristics of ions, including ionic radii and the tendencies of atoms to form cations or anions. Elements are arranged in rows called periods and columns termed groups or families:

• Elements in the same group typically exhibit similar chemical behaviors.
• Cation formation and ionic radius can often be inferred by an element's position on the periodic table.
• For example, elements in the same group often form cations with similar charges.

The position of an element can predict its ionization energy, electronegativity, and the size of its ions, all of which are crucial concepts for understanding ionic radii.

Charge Impact

Charge impact refers to the effect an ion's charge has on its size or radius. When comparing ions, those with a higher positive charge are often smaller due to increased attraction between the electrons and the nucleus. This is because more protons in the nucleus exert a stronger pull on the remaining electrons, reducing the ionic radius.Here are key points about the charge impact:

• The greater the positive charge, the smaller the ionic radius tends to be.
• For example, a doubly charged cation (\( \text{Mg}^{2+} \)) is typically smaller than a single-charge cation (\( \text{Na}^{+} \)).
• The change in charge affects ion size significantly more than just the number of electrons lost.

Charge impact is a crucial factor in determining trends across a period or within a group.

Group 1 and Group 2 Ions

Group 1 and Group 2 ions are characterized by their position on the periodic table. These groups are also known as the alkali metals and alkaline earth metals, respectively. Ions from these groups exhibit important trends in ionic radius and charge.For Group 1 ions:

• These ions, such as \( \text{Na}^+ \) and \( \text{Li}^+ \), typically form by losing one electron, resulting in a +1 charge.
• The loss of this electron leads to a smaller ionic radius compared to their neutral atoms.
• The ions become smaller as you move up the group due to a decrease in electron shells.

Group 2 ions, on the other hand:

• Like \( \text{Mg}^{2+} \) and \( \text{Be}^{2+} \), these ions form by losing two electrons, giving them a +2 charge.
• These ions are typically smaller than Group 1 ions owing to their higher charge, leading to a strong attraction between the nucleus and electrons.
• The effective nuclear charge influences their ionic size significantly, with \( \text{Be}^{2+} \) being smaller than \( \text{Mg}^{2+} \).

Understanding these trends is essential for predicting the behavior and properties of different ionic compounds.