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

Option (a): Mg < Na < K < Rb.

Step 1: Understand Atomic Radius

Atomic radius increases down a group in the periodic table because new electron shells are added, which are further from the nucleus. Across a period, atomic radius typically decreases due to increased nuclear charge, which pulls the electrons closer.

Step 2: Locate Elements in the Periodic Table

Locate the elements Mg, Na, K, and Rb on the periodic table. Mg and Na are in period 3, with Mg to the right of Na. K and Rb are in groups 1-2, with Rb below K. This indicates that Rb and K will have larger radii than Na and Mg.

Step 3: Compare Elements Across a Period

Between Na and Mg, Mg is to the right of Na in the same period. Therefore, Mg has a smaller atomic radius than Na.

Step 4: Compare Elements Down a Group

Rb and K are in the same group (Group 1), with Rb positioned below K. Therefore, Rb has a larger atomic radius than K.

Step 5: Rank the Elements by Atomic Radius

From smallest to largest radius considering the above information: Mg < Na < K < Rb. This is option (a).

Key Concepts

Periodic Table Trends

The periodic table is not just a random collection of elements; it is organized to reveal repeating patterns, also known as "periodic trends." One of the most noticeable trends is the way atomic radius changes as you move across the table.
The atomic radius generally decreases as you move from left to right across a period. This is because, although you are adding more protons and electrons, the increased positive charge from the protons pulls the electrons closer to the nucleus.
On the other hand, as you move down a group, the atomic radius increases. This is because you're adding more electron shells, which are like layers of an onion building outwards from the nucleus. As you add each new shell, the outer electrons become less tightly held by the nucleus.

• Across a period: Atomic radius decreases
• Down a group: Atomic radius increases

These trends are the foundation to predict and compare the sizes of different atoms. Understanding them helps to make sense of chemical properties and reactivity patterns in elements.

Group and Periodic Trends

When looking at the periodic table, elements are arranged in both groups (columns) and periods (rows). Each arrangement exposes different trends in atomic properties. For the atomic radius, these trends can be understood through the "group trends" and "period trends."
Considering 'group trends', elements within the same group often show a progressive increase in atomic radius when going from top to bottom. This increase is because new electron shells are added as we move down, increasing the distance between the outer electrons and the nucleus.
In 'period trends', as you move across a period from left to right, the atomic radius decreases. This decrease is contrary to the group trend because even though electrons are being added to the atoms, they are added to the same electron shell. The simultaneous increase in nuclear charge, with more protons, pulls these electrons more tightly inward.

• Group trends usually show an increasing atomic radius down a group
• Period trends reflect a decrease in atomic radius across a period

These patterns are crucial in predicting how different elements will behave in chemical reactions and bonding.

Element Comparison

When comparing elements, particularly their atomic radii, it's helpful to apply the knowledge of periodic table trends. Let's look at specific comparisons:
Firstly, consider sodium (Na) and magnesium (Mg), which are in the same period. Magnesium is to the right of sodium, meaning it has a smaller atomic radius due to increased nuclear charge pulling its electrons closer.
Now, consider potassium (K) and rubidium (Rb), which are in the same group. Rubidium, below potassium, has a larger atomic radius because an additional electron shell increases the distance between the outer electrons and the nucleus.
Lastly, by comparing elements across these benchmarks, we can rank them. Knowing the periodic trends and applying them, we get the order based on increasing atomic radius:

• Smallest: Magnesium (Mg)
• Na (Sodium)
• K (Potassium)
• Largest: Rb (Rubidium)

This ordering is based on the principles of atomic structure and electric charge dynamics in the periodic table, which are pivotal in understanding the elements’ sizes.