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

Question

The correct order of van der Waals radius of \(\mathrm{F}, \mathrm{Cl}\) 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) \( \text{Br} > \text{Cl} > \text{F} \).

Step 1: Understanding van der Waals radius

Van der Waals radius is a measure of the size of an atom that is not bonded to another atom. It generally increases along down the group of the periodic table as additional electron shells are occupied.

Step 2: Identifying group trend for halogens

Fluorine (0F), chlorine (0Cl), and bromine (0Br) are halogens in Group 17 of the periodic table. As we move down the group from fluorine to chlorine to bromine, the van der Waals radius increases due to the addition of electron shells.

Step 3: Comparing van der Waals radii

Based on the group trend, fluorine has the smallest van der Waals radius, followed by chlorine, and bromine has the largest van der Waals radius.

Step 4: Conclusion on the order of van der Waals radius

The order of van der Waals radius for F, Cl, and Br is Br > Cl > F, which corresponds to option (b).

Key Concepts

Periodic Trends

Periodic trends refer to patterns observed within the periodic table that illustrate various properties of elements as one moves across periods or down groups. One significant periodic trend is the change in atomic or ionic size. As you move down a group in the periodic table, elements tend to gain additional electron shells. This results in larger atomic sizes, as the distance between the nucleus and the outermost electrons increases.
Atomic size isn't the only property affected by periodic trends; other properties include electronegativity, ionization energy, and electron affinity. However, in the context of halogens, particularly for understanding the van der Waals radius, what we primarily observe is the increase in size down the group.

Halogens

Halogens are a group of elements found in Group 17 of the periodic table. The name 'halogen' means "salt-former" and they include five elements: fluorine, chlorine, bromine, iodine, and astatine.
These elements are characterized by having seven valence electrons, which makes them highly reactive as they aim to gain an eighth electron to achieve a stable electron configuration. This reactivity is most pronounced with elements lower on the periodic table, where atomic size is larger. Halogens are known for their strong, distinct odors and their ability to form compounds by reacting with metals and nonmetals alike. Each halogen displays unique properties but all share a common trend in their increasing van der Waals radii due to additional electron shells as you move down the group.

Electron Shells

Electron shells, also known as energy levels, are layers around an atom where its electrons reside. Each shell can hold a specific maximum number of electrons, and as elements increase in atomic number, they add more shells.
For halogens, the number of electron shells increases as you move from fluorine to bromine. This is a direct consequence of adding more electrons and thus, more shells. For instance, fluorine resides in the second period with just two electron shells, while bromine, in the fourth period, possesses four electron shells. This progression results in larger van der Waals radii and demonstrates why bromine's atomic structure is substantially larger than that of fluorine.

Group 17 Elements

Group 17 elements are known for their dramatic chemical behavior and are termed halogens. These elements are nonmetals and possess high electronegativities and high electron affinities. As a result, they vigorously form ionic and covalent bonds to achieve a full set of eight valence electrons.
The properties of Group 17 elements vary significantly as you move down the group. While fluorine is highly corrosive and gaseous at room temperature, iodine is less reactive and exists as a solid. This variation is due to the increasing atomic size and decrease in ionization energies as the electron distance from the nucleus becomes greater. The most notable trend within Group 17 is the increase in van der Waals radius, reflecting the general periodic trends of increasing atomic size due to the addition of electron shells.