📘 Class 12 – Chemistry

Chapter 01: The Solid State ⚪

📌 PART – 2

Welcome back to ExamsPoint Notes, your trusted platform for JEE, NEET, and Board exam handwritten content! This is Part 2 of Class 12 Chemistry Chapter 1: The Solid State, where we dive deeper into the structure and geometry of crystalline solids.

📂 Contents Covered:

✅ Location of Atoms in Unit Cells

Understanding the location of atoms within unit cells is foundational to the study of solid-state chemistry. A unit cell is the smallest repeating structural unit of a crystal lattice and determines the macroscopic physical properties of the crystal. Atoms in a unit cell may occupy corners, face centers, edge centers, or body centers, depending on the type of unit cell.

In a Simple Cubic (SC) unit cell, atoms are positioned only at the eight corners of the cube. Each corner atom is shared among eight neighboring cubes, contributing 1/8 of each atom to the unit cell, resulting in 1 atom per unit cell.
A Body-Centered Cubic (BCC) structure has atoms at all eight corners and a single atom at the center of the cube. Corner atoms contribute 1 atom, and the center atom contributes 1 full atom, totaling 2 atoms per unit cell.
A Face-Centered Cubic (FCC) structure includes atoms at each of the corners and at the centers of all six faces. Each face-centered atom is shared between two unit cells, and corners as usual contribute 1 atom in total, giving a total of 4 atoms per unit cell.
End-Centered Cubic (ECC) unit cells have atoms at each corner and at the centers of two opposite faces, contributing 1 + 2 x 1/2 = 2 atoms per unit cell.

The specific location of atoms impacts the coordination number (number of nearest neighbors), atomic packing factor (APF), and density of the material. These unit cell structures play an essential role in determining the behavior of metals, ionic solids, and other crystalline substances.

✅ Bravais Lattices

The Bravais lattices describe the 14 unique three-dimensional arrangements in which atoms can be systematically placed to form a crystal. These lattices form the framework for all crystalline materials and are grouped into 7 distinct crystal systems, each with specific geometric parameters and angles. The 7 crystal systems include:

Cubic
Tetragonal
Orthorhombic
Monoclinic
Triclinic
Hexagonal
Rhombohedral (Trigonal)

Each of these systems can exhibit one or more of the four types of Bravais lattices: primitive (P), body-centered (I), face-centered (F), and end-centered (C). For example, the cubic system includes three Bravais lattices: simple cubic, body-centered cubic, and face-centered cubic.

Bravais lattices form the fundamental backbone of crystal structures, enabling chemists and material scientists to analyze symmetry, predict physical properties, and categorize materials. Understanding these structures is key to interpreting X-ray diffraction patterns, designing materials with specific properties, and studying phase transitions.

✅ Characteristics of Unit Cells

Unit cells are categorized based on their atomic arrangement into primitive and non-primitive types. A primitive unit cell contains atoms only at the corners of the unit cell. Since each corner atom is shared among eight adjacent unit cells, each contributes 1/8 of an atom, totaling 1 atom per primitive unit cell.

On the other hand, non-primitive unit cells have atoms at additional positions such as the center of the body (body-centered), the centers of the faces (face-centered), or the centers of edges. These additional atoms increase the number of atoms per unit cell and affect the density and packing efficiency.

Another characteristic of unit cells is the coordination number, which indicates the number of nearest neighbors an atom has. For example, SC has a coordination number of 6, BCC has 8, and FCC has 12.

The atomic packing factor (APF), which measures how tightly atoms are packed in a unit cell, also varies with the type: SC has 52.4%, BCC 68%, and FCC the highest at 74%. These characteristics determine the material's mechanical properties, such as hardness, ductility, and tensile strength.

✅ Rank (Z) of a Crystal

The Rank (Z) of a crystal represents the number of atoms per unit cell. It is a critical parameter used in calculating various physical properties like the density of the solid. The Z value differs for different types of unit cells:

Simple Cubic (SC): Z = 1
Body-Centered Cubic (BCC): Z = 2
Face-Centered Cubic (FCC): Z = 4

Knowing the rank is essential for determining the mass of the unit cell, which is calculated as:

$\text{Mass of unit cell} = Z \times M / N_A$

Where:

$Z$ is the number of atoms per unit cell
$M$ is the molar mass
$N_A$ is Avogadro’s number

This value is then used to compute the density using:

$\text{Density} = \frac{\text{Mass of unit cell}}{a^3}$

Where $a$ is the edge length of the unit cell.

✅ Relationships between Edge Length (a), Radius (r), and Interplanar Distance (d)

The edge length $a$ , atomic radius $r$ , and interplanar distance $d$ are interrelated through geometric equations derived from the unit cell structures. These formulas vary based on the type of unit cell:

SC: $a = 2r$
BCC: $a = \frac{4r}{\sqrt{3}}$
FCC: $a = \frac{4r}{\sqrt{2}}$

These relationships are critical for solving problems involving atomic size, unit cell volume, and X-ray diffraction. Interplanar distances are especially important in Bragg’s Law for analyzing crystal structure.

For example, in an FCC structure, atoms are in contact along the face diagonal, which is $\sqrt{2}a$ . Setting this equal to 4r (2 radii per atom, 2 atoms per diagonal) yields $a = \frac{4r}{\sqrt{2}}$ .

Knowing these formulas allows for accurate calculations of atomic radius, density, and other structural parameters essential in materials science and physical chemistry.

📖 Revision Questions

What is the number of atoms in a BCC unit cell?
Define a Bravais lattice. How many types of Bravais lattices are possible?
Derive the formula connecting atomic radius and edge length for an FCC unit cell.
What is the Rank (Z) for a simple cubic structure?
Explain the distinction between primitive and non-primitive unit cells.

📼 Watch the Video Lecture

📓 Visit our YouTube Channel for a detailed visual explanation:
👉 CLICK HERE

📅 Download Full PDF Notes

📌 Get the full set of handwritten notes in PDF format on Telegram:
👉 JOIN TELEGRAM

📧 Request a Chapter

📩 DM us your requests on Instagram:
👉 @examspointnotes

🌐 Follow ExamsPoint Notes

Stay updated with the latest handwritten content:

🔗 YouTube
🔗 Telegram
🔗 Instagram
🔗 Facebook

The Solid States (Part-2) Handwritten Notes and Explanation| Chemistry Class-12 Chapter-1