Problem 14 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The increasing order of the atomic radii of the following elements is: (i) \(\mathrm{C}\) (ii) \(\mathrm{O}\) (iii) F (iv) \(\mathrm{Cl}\) (v) \(\mathrm{Br}\) (a) \((\mathrm{ii})<(\mathrm{iii})<(\mathrm{iv})<(\mathrm{i})<(\mathrm{v})\) (b) \((\mathrm{iv})<(\mathrm{iii})<(\mathrm{ii})<(\mathrm{i})<(\mathrm{v})\) (c) (iii) \(<(i i)<(i)<(i v)<(v)\) (d) \((\mathrm{i})<(\mathrm{ii})<(\mathrm{iii})<(\mathrm{iv})<(\mathrm{v})\)

Step-by-Step Solution

Answer

The correct order is (iii) < (ii) < (i) < (iv) < (v).

Step 1: Understanding Atomic Radii Trends

First, let's understand that atomic radii increase as you move down a group in the periodic table. This is because each subsequent element down a group has an additional electron shell. However, across a period (from left to right), atomic radii decrease due to increasing effective nuclear charge, which pulls the electron cloud closer to the nucleus.

Step 2: Identify Element Positions

Locate the given elements: C (Carbon), O (Oxygen), F (Fluorine) are in Period 2, moving from left to right. Cl (Chlorine) and Br (Bromine) are in Period 3 and 4, respectively, and are positioned further down in Group 17 (halogens).

Step 3: Compare Group Trends

Among elements in the same group (like F, Cl, and Br), Br has the largest atomic radius, followed by Cl, and then F has the smallest.

Step 4: Compare Period Trends

Within Period 2, when moving from C to O to F, the atomic radius decreases: C > O > F. This is due to increasing nuclear charge that pulls electrons closer, reducing the size.

Step 5: Order Elements by Size

Consider that Br > Cl, C > O > F from the above analyses. Combining period and group trends, the correct increasing order of atomic radii is F < O < C < Cl < Br.

Key Concepts

Periodic Table

The periodic table is a powerful tool in chemistry that arranges elements in a systematic order. It is based on their atomic number, which is the number of protons in an atom's nucleus. Elements are organized into rows called "periods" and columns known as "groups."

• Rows or periods: Elements within the same row share the same number of electron shells. As you move from left to right in a period, the atomic number increases.
• Columns or groups: Elements in the same column have similar chemical properties because they have the same number of valence electrons, which are the electrons in the outermost shell.

Understanding the periodic table is crucial for predicting atomic radii trends. As you progress down a group, new electron shells are added. This causes the atomic radius to increase. Contrarily, when moving from left to right across a period, the effective nuclear charge increases, resulting in smaller atomic radii.

Effective Nuclear Charge

Effective nuclear charge (often symbolized as \(Z_{eff}\)) is an important concept to grasp when studying atomic structure. It refers to the net positive charge experienced by valence electrons in an atom. Essentially, it represents the pull exerted by the nucleus on the electrons.Here is how it affects atomic radii:

• Across a period, the effective nuclear charge increases because more protons are added to the nucleus while additional electrons are added to the same shell. This causes the electrons to be pulled closer to the nucleus, which decreases the size of the atom.
• The greater the effective nuclear charge, the smaller the atomic radius, as the electron cloud is drawn closer to the nucleus.

This phenomenon explains why the atomic radii across a period decrease, as seen when comparing elements like carbon to fluorine in Period 2.

Halogens

Halogens are a unique group in the periodic table, specifically Group 17. They are known for their high reactivity and are essential elements in chemical reactions due to their ability to gain an electron to achieve a full valence shell. Some characteristics of halogens include:

• They have seven valence electrons, making them one electron short of a complete octet, which is why they readily form negative ions.
• The atomic radii of halogens increase down the group. Starting from the top with fluorine, chlorine, bromine, and so forth, each element adds an extra electron shell. As a result, bromine has a larger atomic radius than chlorine and fluorine.

Understanding the trends in atomic radii among halogens helps us predict their behavior in chemical reactions and their relative sizes.

Electron Shells

Electron shells are layers around the nucleus of an atom where electrons are likely to be found. The arrangement of these shells defines the size and shape of an atom. Key points about electron shells include:

• Each shell can hold a certain maximum number of electrons: for example, the first shell can hold up to 2, the second up to 8, and so on.
• When moving down a group in the periodic table, each step adds a new electron shell. This increases the overall size of the atom, leading to a larger atomic radius.

Thus, as elements like bromine are further down the group compared to fluorine and chlorine, they have more electron shells. This results in a larger distance between the nucleus and its valence electrons, contributing to a larger atomic radius.