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

Question

The set representing the correct order of ionic radius is: (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

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

Step 1: Understanding Ionic Radius

The ionic radius is the measure of an atom's ion in a crystal lattice. Generally, cations (positive ions) are smaller than their neutral atoms because they lose electrons and minimize the electron-electron repulsion.

Step 2: Compare Cations in the Same Group

When comparing cations within the same group of the periodic table, the ionic radius decreases with an increasing number of protons. For example, - \(\mathrm{Na}^+\) and \(\mathrm{Li}^+\) are in Group 1. \(\mathrm{Li}^+\) is smaller than \(\mathrm{Na}^+\) because it has fewer electron shells.

Step 3: Compare Cations with Different Charges

Cations with higher positive charges are generally smaller because they lose more electrons. For example, - \(\mathrm{Mg}^{2+}\) and \(\mathrm{Be}^{2+}\) are in Group 2. \(\mathrm{Be}^{2+}\) is smaller than \(\mathrm{Mg}^{2+}\) partly due to having higher nuclear charge acting on fewer electrons as compared to other elements with the same charge.

Step 4: Conclude Correct Order of Ionic Radius

We combine our understanding from previous steps: - \(\mathrm{Na}^+ (cation in Group 1) > \mathrm{Li}^+ (cation in Group 1) > \mathrm{Mg}^{2+} (cation in Group 2) > \mathrm{Be}^{2+} (cation in Group 2)\)Hence, the correct order is: \(a) \mathrm{Na}^{+} > \mathrm{Li}^{+} > \mathrm{Mg}^{2+} > \mathrm{Be}^{2+}\).

Key Concepts

Cations

Cations are positively charged ions formed when an atom loses one or more electrons. This electron loss results in a net positive charge, transforming the neutral atom into a cation. The formation of a cation usually happens to achieve a stable electron configuration, often similar to the nearest noble gas.

When comparing cations to their parent atoms, they are typically smaller in size. The reduction in size occurs because the loss of electrons decreases electron-electron repulsion, pulling the remaining electrons closer to the nucleus. This shrinkage is more pronounced in cations than in neutral atoms or anions, which tend to gain electrons rather than lose them.

For example:

• When sodium (Na) loses an electron, it becomes Na^+ and significantly smaller.
• Similarly, lithium (Li) forms Li^+ by losing one electron, reducing its size considerably.

Understanding the nature of cations helps in predicting ionic sizes and behaviors in chemical reactions.

Ionic size comparison

Ionic size plays a crucial role in determining the properties of ions. When comparing the sizes of different cations, several factors, such as charge and electron configuration, must be considered. Generally, ions with the same charge can be compared by their atomic numbers and their position in the periodic table.

When cations possess different charges, the size is influenced by the magnitude of the charge. Higher positive charges tend to decrease the ionic radius because of greater attraction between the electrons and the nucleus. As a result, you observe that

• Mg^{2+} is smaller than Na^+ due to its higher charge and stronger pull by the positively charged nucleus.
• Be^{2+} is even smaller than Mg^{2+} for the same reason, combined with fewer electron shells.

When comparing cations with the same charge but different atomic numbers, cations from the same group, those with fewer electron shells (like Li^+), are smaller than those with more (like Na^+). Understanding these trends is key to correctly determining ionic sizes.

Periodic table trends

The periodic table is a systematic arrangement of elements that exhibits clear trends in properties based on atomic structure. These trends are evident in ionic sizes, which are crucial in understanding chemical behavior.

The main trends that affect the ionic radius include:

• Atomic Number: As you move from left to right across a period, the number of protons increases, pulling electrons closer and reducing ionic size.
• Group Trends: Moving down a group, elements have more electron shells, resulting in larger atomic and ionic radii, as seen moving from Li^+ to Na^+.
• Ionization and Charge: Elements that form higher charged cations, like Mg^{2+}, exhibit smaller radii compared to singly charged ions like Na^+.

These periodic trends simplify the prediction of properties and reactivities of elements, helping to identify the position of an element like Na^+, Li^+, Mg^{2+}, or Be^{2+} in the context of ionic size. Understanding these trends enhances comprehension of elemental characteristics and reactions.