Problem 16 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Which one of the following statements about packing in solids is incorrect? (a) Coordination number in \(b c c\) mode of packing is 8 . (b) Coordination number in hcp mode of packing is \(12 .\) (c) Void space in \(h c p\) mode of packing is \(32 \%\). (d) Void space is \(c c D\) mode of packing is \(26 \%\)

Step-by-Step Solution

Answer

Statement (c) is incorrect; hcp packing has 26% void space, not 32%.

Step 1: Understand the Types of Packing

In solids, atoms are packed in different arrangements known for their unique properties. The common types include body-centered cubic (bcc), hexagonal close-packed (hcp), and cubic close-packed (sometimes referred to as face-centered cubic, fcc). Understanding these packing types and their characteristics such as coordination number and void space is crucial.

Step 2: Review Coordination Numbers

The coordination number is the number of nearest neighbors surrounding an atom in a crystal lattice. For bcc, the coordination number is 8. For hcp and fcc, the coordination number is 12. Therefore, statements (a) and (b) are correct as per the given values of coordination numbers.

Step 3: Understand Void Space in Packing

The void space or efficiency of packing refers to the volume of unoccupied spaces in the crystal lattice. In hcp and fcc, the packing efficiency is approximately 74%, leaving 26% as void space. For bcc, the packing efficiency is around 68%, resulting in approximately 32% void space. This indicates statement (c) is incorrect because it claims the void space in hcp is 32% instead of 26%.

Step 4: Re-evaluate Each Statement

Let's re-evaluate: (a) Correct, since coordination number in bcc is indeed 8. (b) Correct, as hcp has a coordination number of 12. (c) Incorrect, because hcp should have a 26% void space, not 32%. (d) Correct, since void space in ccd (fcc) is 26%.

Key Concepts

Coordination Number

In solid state chemistry, the coordination number is an important concept. It refers to the number of atoms directly surrounding a central atom in a crystal lattice. Think of it as the number of neighbors an atom has in its structure.
For example:

• In a body-centered cubic (bcc) structure, each atom is surrounded by 8 other atoms, so the coordination number is 8.
• For hexagonal close-packed (hcp) and cubic close-packed (ccp), also known as face-centered cubic (fcc), the coordination number is 12. This is because each atom is closely packed with 12 neighbors.

The coordination number is key in determining the stability and physical characteristics of the structure.

Void Space

Void space refers to the empty areas within a crystal lattice that are not occupied by atoms. It is a measure of how efficiently atoms are packed together in the structure.
Atoms in a crystal lattice do not occupy the entire volume, leaving some void space. The efficiency of packing and the percentage of void space are essentially about how tightly the atoms are packed.
For instance:

• In the hexagonal close-packed (hcp) and face-centered cubic (fcc), about 74% of the space is occupied by atoms, leaving 26% as void space.
• In body-centered cubic (bcc) packing, the atoms occupy around 68% of the space, resulting in approximately 32% void space.

Understanding void space helps predict the density and other properties of a material.

Crystal Lattice Packing

Crystal lattice packing describes how atoms are systematically arranged in solids. This arrangement affects physical properties such as density and stability. The primary types of packing include body-centered cubic (bcc), hexagonal close-packed (hcp), and cubic close-packed (ccp or fcc).

Some key points include:

• Hexagonal close-packed (hcp) has a hexagonal arrangement where layers of atoms are stacked closely together. It allows maximum packing efficiency.
• Body-centered cubic (bcc) has each atom at the center of the cube structure, providing a unique arrangement.

Studying these packing types helps understand how materials can behave mechanically and thermally.

Body-Centered Cubic

The body-centered cubic (bcc) structure is one of the simpler types of crystal lattices. In a bcc structure, each atom is positioned at the center of a cube made up of eight other atoms.

This structure has certain characteristics:

• It has a coordination number of 8, meaning each central atom is surrounded by 8 neighboring atoms.
• The packing efficiency is about 68%, which means the void space is about 32%.

The bcc structure is less densely packed compared to fcc or hcp, but it is still a very common packing arrangement found in metals such as iron, chromium, and tungsten.

Hexagonal Close-Packed

The hexagonal close-packed (hcp) structure is defined by the way atoms are arranged in a hexagonal pattern, optimizing the space they occupy. It is prominent in metals like magnesium and titanium.

Here's what makes hcp unique:

• Its coordination number is 12, indicating each atom is closely surrounded by 12 other atoms.
• The packing efficiency is high, around 74%, meaning the void space is a small 26%.

This efficient packing allows hcp structures to have high density and strong bonding, leading to good mechanical strength.