Problem 22 - A Complete Resource Book in Chemistry for JEE Main

Question

The increasing order of atomic radius for the elements \(\mathrm{Na}, \mathrm{Rb}, \mathrm{K}\) and \(\mathrm{Mg}\) is (a) \(\mathrm{Mg}<\mathrm{Na}<\mathrm{K}<\mathrm{Rb}\) (b) \(\mathrm{Rb}<\mathrm{K}<\mathrm{Mg}<\mathrm{Na}\) (c) \(\mathrm{Na}<\mathrm{K}<\mathrm{Mg}<\mathrm{Rb}\) (d) \(\mathrm{Na}<\mathrm{Mg}<\mathrm{K}<\mathrm{Rb}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{Mg}<\mathrm{Na}<\mathrm{K}<\mathrm{Rb}\)."

Step 1: Understanding Atomic Radius

The atomic radius is the distance from the center of the nucleus to the outermost electron shell. It generally increases as you move down a group in the periodic table because each element down a group has an additional electron shell. Across a period from left to right, the atomic radius generally decreases due to the increase in nuclear charge, which pulls the electron cloud closer to the nucleus.

Step 2: Identify Group Positions

Determine the group and period positions of the elements involved. Sodium (Na) and Magnesium (Mg) are in the 3rd period, with Na in Group 1 and Mg in Group 2. Potassium (K) is in Group 1 of the 4th period. Rubidium (Rb) is in Group 1 of the 5th period.

Step 3: Comparing Atomic Radii by Group

Since Na, K, and Rb are in the same group (Group 1), they can be directly compared based on their periods. Atomic radius increases down the group: \(\mathrm{Na} < \mathrm{K} < \mathrm{Rb}\).

Step 4: Comparing Period 3 Elements

Now compare Na and Mg, both in period 3 but in different groups. Na (Group 1) has a larger atomic radius than Mg (Group 2) due to a smaller nuclear charge effect in Na compared to Mg: \(\mathrm{Mg} < \mathrm{Na}\).

Step 5: Compile the Order

Compile the findings to determine the correct increasing order, starting with the smallest radius: \(\mathrm{Mg} < \mathrm{Na} < \mathrm{K} < \mathrm{Rb}\). This corresponds to option (a).

Key Concepts

Periodic Table Trends

When considering atomic radii, periodic table trends offer essential insights. As we move from left to right across a period, elements experience a decrease in their atomic radius. This is because the number of protons increases, leading to a higher nuclear charge, which pulls the outer electrons closer to the nucleus. On the other hand, moving down a group results in an increase in atomic radius. This is due to the addition of electron shells which outweighs the increase in nuclear charge, making the atoms larger.

Here are some key takeaways about periodic table trends for atomic radius:

• Atomic radius decreases across a period from left to right.
• Atomic radius increases down a group in the periodic table.
• The nuclear charge's effect is a dominant factor across periods, but electron shielding becomes more important down a group.

Group and Period Positions

Understanding the position of elements within groups and periods is fundamental when analyzing atomic radii. The periodic table is structured to show elements of similar properties in vertical columns known as groups, and horizontal rows referred to as periods. Each group and period provides clues about the elements' atomic structure, affecting their size significantly.

Let's consider the positions of the elements in question:

• Sodium (Na) and Magnesium (Mg) are both in the 3rd period. Mg is in Group 2 (alkaline earth metals), and Na is in Group 1 (alkali metals).
• Potassium (K) is in Group 1 and the 4th period.
• Rubidium (Rb) is also in Group 1 but is found in the 5th period.

As we identify these positions, it helps explain why Mg is smaller than Na despite being in the same period. The increased nuclear charge in Mg pulls its electrons closer, reducing its atomic radius.

Comparative Atomic Radii

Comparing atomic radii within the same group or period helps us understand their relative sizes. In the case of Group 1 elements like Na, K, and Rb, we observe a clear trend: atomic radius increases as we move down the group. This is because each subsequent element adds a new electron shell, making the atom larger overall.

For Na and Mg, which are both in the 3rd period but different groups (Na in Group 1 and Mg in Group 2), comparing their atomic radii requires considering both nuclear charge and additional electronic shielding. Na ends up with a larger atomic radius than Mg because its nuclear charge is lower, allowing its electrons to spread out more.

• Within Group 1: \( ext{Na}\) is smaller than \( ext{K}\), and \( ext{K}\) is smaller than \( ext{Rb}\).
• Within Period 3: \( ext{Mg}\) is smaller than \( ext{Na}\).

Nuclear Charge Effect

The nuclear charge effect plays a pivotal role in determining an atom's radius. As the number of protons in the nucleus increases, so does the nuclear charge. This charge influences how tightly electrons are held within the atom. Within a period from left to right, the increasing nuclear charge draws electrons in closer, thereby reducing the atomic radius.

The different groups exhibit varying nuclear charge effects, as seen when comparing elements like Mg and Na in the same period. Mg has a higher nuclear charge due to having more protons, which pulls its electrons closer, resulting in a smaller atomic radius compared to Na.

Essential points regarding the nuclear charge effect include:

• A higher nuclear charge results in a smaller atomic radius across a period.
• Nuclear charge has a lesser impact down a group due to increased electron shielding.
• Understanding nuclear charge helps predict comparative atomic sizes among elements.