Problem 8 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of atomic radii is (a) \(\mathrm{F}<\mathrm{K}<\mathrm{Na}<\mathrm{Li}\) (b) \(\mathrm{Li}<\mathrm{Na}<\mathrm{K}<\mathrm{F}\) (c) \(\mathrm{F}<\mathrm{Li}<\mathrm{Na}<\mathrm{K}\) (d) \(\mathrm{Na}<\mathrm{K}<\mathrm{Li}<\mathrm{F}\)

Step-by-Step Solution

Answer

The correct order of atomic radii is: (c) \( \mathrm{F}<\mathrm{Li}<\mathrm{Na}<\mathrm{K} \).

Step 1: Understand the Periodic Trend

Atomic radius tends to increase as you move down a group in the periodic table because additional electron shells are added. Conversely, as you move across a period from left to right, the atomic radius generally decreases due to the increase in nuclear charge pulling the electrons closer to the nucleus.

Step 2: Identify the Elements' Group and Period

Fluorine (F) is in Group 17 (halogens) and the second period. Lithium (Li) is in Group 1 and the second period. Sodium (Na) is in Group 1 and the third period. Potassium (K) is in Group 1 and the fourth period.

Step 3: Analyze the Atomic Radii Based on Periodic Trends

Among the given elements, K and Na are both in Group 1 but different periods, with K below Na, so K will have a larger atomic radius than Na. Li is also in Group 1, but in an earlier period than Na, giving it a smaller atomic radius than Na. Fluorine, in a different group and period, has the smallest atomic radius because it is on the rightmost side and topmost of its period.

Step 4: Order the Atomic Radii

Fluorine (F) has the smallest atomic radius, followed by lithium (Li), then sodium (Na), and finally potassium (K), which has the largest. This order of increasing atomic radius is: F < Li < Na < K.

Key Concepts

Periodic Table Trends

The periodic table is a useful tool for predicting the properties of elements, including their atomic radii. Atomic radii denote the size of an atom and are influenced by the element's position on the periodic table. Let's explore these trends:

• Down a Group: As we move down a group, atomic radii increase. This is because each successive element adds a new electron shell, making the atom larger.
• Across a Period: Moving from left to right across a period, the atomic radii decrease. Although electrons are added, they are being pulled closer to the nucleus due to increasing nuclear charge, thus reducing the atomic size.
• General Observations: Larger atoms have more electron layers, while smaller atoms have fewer. Thus, position in the table determines whether an atom is likely to be larger or smaller.

Atomic Structure

The atomic structure of an element defines its physical and chemical properties, including its atomic radius. Here’s what you need to know:

• Atomic Nucleus: The central part of the atom, composed of protons and neutrons. This nucleus is positively charged due to the protons, affecting the electrons' arrangement around it.
• Electron Shells: Electrons orbit the nucleus in shells. The number of these shells increases as we move down the periods in the periodic table. More shells mean greater atomic radius.
• Effective Nuclear Charge: This refers to the net positive charge experienced by electrons. As the effective nuclear charge increases (across a period), the electrons are pulled closer to the nucleus, reducing the atomic radius.

Understanding atomic structure helps explain why atomic radii change in predictable ways depending on an element's place in the periodic table.

Group and Period Classification

Classifying elements into groups and periods is essential for predicting atomic radius trends. Here’s how this classification works:

• Groups: Vertical columns on the periodic table indicate the group, characterized by the same number of valence electrons. For instance, lithium (Li), sodium (Na), and potassium (K) are all in Group 1, and they trend toward larger atomic radii as we move down the group.
• Periods: Horizontal rows signify periods. Each period indicates elements have their electrons filling the same principal energy level. As you move across a period from left to right, atomic radii decrease due to increasing nuclear charge.
• Trends Application: Understanding the relationship between groups and periods assists in anticipating atomic radius changes. For example, elements in higher periods and closer to the left of the table have larger radii, while those more right and top have smaller radii.

Learning these classifications can help predict and explain different atomic properties, such as size, for any element.