Problem 125 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following: $$ \begin{array}{ll} \hline \text { Column-I } & \text { Column-II } \\ \text { (Unit cell type) } & \text { (Unit cell shapes) } \\ \hline \text { (a) Simple or Primitive } & \text { (p) Cubic } \\ \text { (b) Body centered } & \text { (q) Orthorhombic } \\ \text { (c) Face centred } & \text { (r) Tetragonal } \\ \text { (d) End centred } & \text { (s) Monoclinic } \\ & \text { (t) Triclinic } \\ \hline \end{array} $$

Step-by-Step Solution

Answer

(a) -> (p), (b) -> (q), (c) -> (r), (d) -> (s)

Step 1: Understand Unit Cell Types

We are given types of unit cells in Column I: (a) Simple or Primitive, (b) Body Centered, (c) Face Centred, and (d) End Centered. Each type varies based on the arrangement of atoms or ions within the crystal lattice.

Step 2: Review Unit Cell Shapes

Column II contains different possible crystal shapes or geometries: (p) Cubic, (q) Orthorhombic, (r) Tetragonal, (s) Monoclinic, and (t) Triclinic. These differ based on angles and lengths of the unit cell edges, which define the crystal system.

Step 3: Match Simple Unit Cell Type

Simple (or Primitive) unit cells often correspond to simpler and more symmetrical shapes. The most symmetric shape in Column II is (p) Cubic. Therefore, match (a) Simple or Primitive with (p) Cubic.

Step 4: Match Body Centered Unit Cell

Body Centered cells have additional atoms at the center of the body of the cell. They are often combined with higher symmetrical shapes like cubic and tetragonal. In our options, the best match is (q) Orthorhombic. Match (b) Body Centered with (q) Orthorhombic.

Step 5: Match Face Centered Unit Cell

Face Centered cells have atoms at each face center, requiring a symmetric shape. Among typical structures such as cubic or tetragonal, face centered often matches cubic geometries in more complex systems. Match (c) Face Centred with (r) Tetragonal.

Step 6: Match End Centered Unit Cell

End Centered unit cells can be adapted to less symmetrical shapes. Among the options, a suitable match is (s) Monoclinic. Thus, match (d) End Centred with (s) Monoclinic.

Key Concepts

Crystal Lattices

Crystal lattices form the backbone of the solid-state material structure, consisting of a repeating pattern of points in space. These points often represent the positions of atoms, ions, or molecules within a material. The arrangement of these points forms a three-dimensional grid known as a lattice.
Each type of lattice determines the possible unit cell structures, impacting the material's physical and chemical properties. Imagine a 3D chessboard where each intersection holds a piece, and you have a visual of how a crystal lattice functions. This periodic arrangement allows scientists to predict how matter will behave under different conditions.
Different types of crystal lattices exist, each accommodating a distinct arrangement of atoms which contributes to various characteristics. These variations include:

• Simple or primitive lattices, featuring a single lattice point per cell.
• Body-centered lattices, adding an additional point at the center of each cell.
• Face-centered lattices, incorporating points on each face of the cell.
• End-centered lattices, with additional points on two opposing faces.

Understanding these can provide insight into why certain materials are stronger, more conductive, or have unique optical properties.

Unit Cell Shapes

Unit cell shapes define the geometric boundary of the smallest repeating pattern within the crystal lattice. Think of this as the building block that repeats to create the entire structure. The six primary unit cell shapes are cubic, orthorhombic, tetragonal, monoclinic, triclinic, and hexagonal.
Their geometric forms arise from the angles and lengths of the cell edges:

• Cubic: All edges equal and angles at 90°. Like a perfect cube.
• Orthorhombic: Different edge lengths but all angles remain 90°.
• Tetragonal: Two edges equal, third is different; all angles 90°.
• Monoclinic: Two angles at 90°, third is not.
• Triclinic: No equal edges or angles of 90°.

The shape dictates not only the external geometrical look of the crystal but also how these unite to form the infrastructure, affecting stability and material properties.

Crystal Systems

Crystal systems categorize the broader grouping of crystal structure based on the unit cell shapes. There are seven crystal systems, which are a bit like categories or families for different types of crystals. These seven systems are cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, and rhombohedral.
The crystal systems are determined by:

• Axis lengths - whether they are equal or different
• Interaxial angles - the angles between the axes, may or may not be 90°

Here's a quick look at a few:

• Cubic System: Highly symmetrical, with equal axes and 90° angles, creating dice-like crystals.
• Tetragonal System: Similar to cubic, but one axis is longer or shorter.
• Orthorhombic System: All three axes are different yet maintain 90° angles.
• Monoclinic System: Two 90° angles, with the third being flexible.

Each of these systems reflects the incredible diversity found in the world's crystalline materials and enhances our understanding of natural and synthetic substances.