Problem 102 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of van der Waals radius of F, Cl and \(\mathrm{Br}\) is (a) \(\mathrm{Cl}>\mathrm{F}>\mathrm{Br}\) (b) \(\mathrm{Br}>\mathrm{Cl}>\mathrm{F}\) (c) \(\mathrm{F}>\mathrm{Cl}>\mathrm{Br}\) (d) \(\mathrm{Br}>\mathrm{F}>\mathrm{Cl}\)

Step-by-Step Solution

Answer

The correct order is (b) \( \mathrm{Br} > \mathrm{Cl} > \mathrm{F} \).

Step 1: Understanding van der Waals Radius

The van der Waals radius of an atom is a measure of its size, calculated based on the distances between non-bonded atoms in a molecule. In general, within the same group in the periodic table, the van der Waals radius increases as you move down because additional electron shells are added.

Step 2: Identifying Elements and Their Periodic Groups

Fluorine (F), Chlorine (Cl), and Bromine (Br) are all halogens that belong to Group 17 of the periodic table. As you move down this group from F to Cl to Br, the van der Waals radius is expected to increase due to the addition of electron shells.

Step 3: Application of Trend in Van der Waals Radii

Based on the trend in Group 17, the van der Waals radii should follow the order: Bromine will have the largest radius, followed by Chlorine, and Fluorine should have the smallest.

Step 4: Selecting the Correct Answer

From the observed trend, the correct order of van der Waals radii should be: Br > Cl > F. Look at the options provided: (b) \( \mathrm{Br} > \mathrm{Cl} > \mathrm{F} \) reflects this order.

Key Concepts

Periodic Table Trends

Periodic table trends refer to predictable patterns observed across elements organized in the periodic table. One such trend is the change in atomic radius as you move down a group. For instance, when you move down the halogen group (Group 17), which includes fluorine (F), chlorine (Cl), and bromine (Br), each succeeding element has an additional electron shell compared to the one above it. This results in effectively increasing the atomic size despite the greater positive charge in the nucleus pulling on more electrons.

Key trends to be aware of include:

• Atomic Radius: Increases as you move down a group due to additional electron shells.
• Ionization Energy: Generally decreases down a group since the outer electrons are further from the nucleus.
• Electronegativity: Typically decreases down a group as the increased distance from the nucleus reduces the attraction for outer electrons.

Understanding these trends helps predict and explain behaviors of elements and their chemical properties.

Halogens

Halogens are a group of five nonmetals in Group 17 of the periodic table, including fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At). They are known for their high reactivity, particularly with alkali and alkaline earth metals, forming stable ionic crystals known as salts.

A few notable characteristics of halogens:

• Reactivity: Highly reactive, becoming less so down the group due to decreasing electronegativity.
• State at Room Temperature: Varies down the group - fluorine is a gas, chlorine is a gas, bromine is a liquid, and iodine is a solid.
• Color: The color of halogens becomes darker moving down the group; for example, fluorine is pale yellow, whereas iodine is shimmering purple.

The unique properties of halogens make them essential in various chemical industries, including in the synthesis of polymers and as disinfectants and bleaching agents.

Electron Shells

The concept of electron shells is fundamental in understanding atomic structure and periodic trends. Electron shells are layers of orbitals surrounding the nucleus where electrons are likely to be found. These shells are labeled as K, L, M, N, etc., moving outward from the nucleus.

Each shell holds a specific number of electrons, dictated by the formula 2n², where n represents the shell level. For instance, the first shell (K) can hold up to 2 electrons, the second (L) up to 8, and so on.

Electron shells are crucial for:

• Determining Chemical Properties: The configuration within these shells, particularly the outermost (valence) shell, determines an atom's reactivity and how it bonds with other atoms.
• Atomic Radius Trends: As you progress to elements with more shells, the atomic radius increases because the outermost electrons are further from the nucleus.
• Energy Levels: Electrons in shells closer to the nucleus have lower energy compared to those further away, affecting how easily they can be removed or shared in chemical reactions.

Understanding electron shells helps students grasp why atoms behave the way they do and predict their interactions with one another.