Problem 18 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The correct order of the atomic radii of \(\mathrm{C}, \mathrm{Cs}, \mathrm{Al}\), and \(\mathrm{S}\) is : (a) \(\mathrm{C}<\mathrm{S}<\mathrm{A} 1<\mathrm{Cs}\) (b) \(\mathrm{S}<\mathrm{C}<\mathrm{Cs}<\mathrm{Al}\) (c) \(\mathrm{S}<\mathrm{C}<\mathrm{Al}<\mathrm{Cs}\) (d) \(\mathrm{C}<\mathrm{S}<\mathrm{Cs}<\mathrm{Al}\)

Step-by-Step Solution

Answer

The correct order of atomic radii is option (c): \( \mathrm{C} < \mathrm{S} < \mathrm{Al} < \mathrm{Cs} \).

Step 1: Periodic Trends Recap

The atomic radius is a measure of the size of an atom from its nucleus to the outer boundaries of its surrounding cloud of electrons. Atomic radii tend to increase as you move down a group in the periodic table due to the addition of electron shells. Conversely, atomic radii tend to decrease as you move across a period from left to right due to increased nuclear charge which pulls the electrons closer to the nucleus.

Step 2: Identify Element Positions

Identify the positions of the elements on the periodic table: Carbon (C) is in Group 14 and Period 2, Sulfur (S) is in Group 16 and Period 3, Aluminum (Al) is in Group 13 and Period 3, and Cesium (Cs) is in Group 1 and Period 6. Based on their positions, we can predict their relative sizes.

Step 3: Apply Group and Period Trends

Observation indicates that members of a group (downwards direction) increase in size, and members of a period (left to right direction) typically decrease in size. Hence, Cesium (in a much lower period) is expected to have the largest radius, and Carbon (in a higher period) is likely to have the smallest radius, while Aluminum and Sulfur, being in the same period, need further differentiation.

Step 4: Compare Intra-Period Elements

Between Aluminum and Sulfur, which are in Period 3, Aluminum is to the left of Sulfur on the periodic table. Therefore, Aluminum, having fewer protons than Sulfur, is less effective in pulling the electron cloud inward, leading to a larger atomic radius for Aluminum than for Sulfur.

Step 5: Determine Correct Order

From our analysis: Carbon (C) < Sulfur (S) < Aluminum (Al) < Cesium (Cs) reflects the correct order of increasing atomic radii. This aligns with answer choice (c).

Key Concepts

Atomic Radius

The atomic radius is essentially the size of an atom, from the core of its nucleus to the outer edge of its electron cloud. This measurement helps us understand how atoms interact with one another. A bigger atomic radius means an atom takes up more space, while a smaller radius indicates the atom is more compact. The factors that affect an atom's radius include the number of electronic shells and the effective nuclear charge.

• As you go down a group in the periodic table, atoms gain more electron shells, thus increasing the atomic radius.
• Conversely, as you move across a period from left to right, the atomic radius decreases. This phenomenon occurs because the increased positive charge of the nucleus pulls the electron cloud closer, making the atom tighter and smaller.

Understanding the atomic radius helps us predict how different elements will interact, bond, and stack in various materials.

Periodic Table

The periodic table is an organized map of the chemical elements. It arranges elements based on their atomic number, which is the number of protons in an atom's nucleus. This visualization helps scientists and students alike to see patterns and relationships among elements, known as periodic trends.

• Groups are the vertical columns that share common properties, as they have the same number of electrons in their outer shell.
• Periods are the horizontal rows where elements have the same number of electron shells.

By examining an element's group and period, we can predict certain chemical behaviors, like how it reacts with other elements or how big its atomic radius might be.

Group Trends

Group trends in the periodic table show how properties change when moving down a vertical column, or group. Understanding these trends helps predict the behavior of elements that are in the same group. One of the key group trends is the change in atomic radius. As you move down a group:

• The atomic radius increases due to the addition of electron shells, making the atom larger.
• The outermost electrons feel less pull from the nucleus because they are further away, which can affect an element’s reactivity.

These factors influence not only atomic size but other properties such as ionization energy and electron affinity. These patterns are crucial in understanding the chemical nature of the elements in a group.

Period Trends

Period trends refer to changes that occur in elements across a horizontal row of the periodic table. These trends influence numerous properties, one prominent example being the atomic radius. Moving across a period from left to right:

• The atomic radius decreases because the number of protons in the nucleus increases, which pulls the electron cloud closer to the nucleus.
• Elements also become less metallic as they gain more electrons in their outer shell, affecting their chemical reactivity.

These regular shifts in the characteristics of elements are what make the periodic table a powerful tool for predicting the behavior of elements, allowing chemists to infer reactivity, conductivity, and even how they might bond with other elements.