Chapter 12, Problem 74A

Interpretation Introduction

(a)

Interpretation:

The shape of the crystal with same edge lengths and face angles needs to be determined.

Concept introduction:

There are a number of factors on which the shapes of crystals depend. These factors are the length and size of their surfaces and edges as well as their face angles. The shape is named after their geometry. The main seven types of crystals are as follows:

• Cubic
• Orthorhombic
• Monoclinic
• Triclinic
• Trigonal
• Hexagonal
• Tetragonal

Answer to Problem 74A

Cubic structure.

Explanation of Solution

The given lengths are as follows:

$\begin{array}{l}a=\text{3 nm}\\ b=\text{3 nm}\\ c=\text{3 nm}\end{array}$

Also, the face angles are as follows:

$\begin{array}{l}\alpha ={90}^{\text{o}}\\ \beta ={90}^{\text{o}}\\ \gamma ={90}^{\text{o}}\end{array}$

Here, all the bond lengths are equal and face angles are also equal thus, this represents the cubic structure.

Interpretation Introduction

(b)

Interpretation:

The shape of the crystal needs to be determined.

Concept introduction:

There are a number of factors on which the shapes of crystals depend. These factors are the length and size of their surfaces and edges as well as their face angles. The shape is named after their geometry. The main seven types of crystals are as follows:

• Cubic
• Orthorhombic
• Monoclinic
• Triclinic
• Trigonal
• Hexagonal
• Tetragonal

Answer to Problem 74A

Monoclinic crystals.

Explanation of Solution

The given lengths are as follows:

$\begin{array}{l}a=\text{4 nm}\\ b=\text{3 nm}\\ c=5\text{ nm}\end{array}$

Also, the face angles are as follows:

$\begin{array}{l}\alpha ={90}^{\text{o}}\\ \beta ={100}^{\text{o}}\\ \gamma ={90}^{\text{o}}\end{array}$

Here, all the edge lengths are different. Also, two face angles are same. Therefore, it represents monoclinic crystals.

Interpretation Introduction

(c)

Interpretation:

The shape of the crystal with given edge lengths and face angles needs to be determined.

Concept introduction:

There are a number of factors on which the shapes of crystals depend. These factors are the length and size of their surfaces and edges as well as their face angles. The shape is named after their geometry. The main seven types of crystals are as follows:

• Cubic
• Orthorhombic
• Monoclinic
• Triclinic
• Trigonal
• Hexagonal
• Tetragonal

Answer to Problem 74A

Tetragonal.

Explanation of Solution

The given lengths are as follows:

$\begin{array}{l}a=3\text{ nm}\\ b=\text{3 nm}\\ c=5\text{ nm}\end{array}$

Also, the face angles are as follows:

$\begin{array}{l}\alpha ={90}^{\text{o}}\\ \beta ={90}^{\text{o}}\\ \gamma ={90}^{\text{o}}\end{array}$

Here, two edge lengths are the same and the third one has the greatest value. All the face angles are at 90^o to each other. Therefore, it represents tetragonal.

Interpretation Introduction

(d)

Interpretation:

The shape of the crystal using given values of edge lengths and face angles needs to be determined.

Concept introduction:

There are a number of factors on which the shapes of crystals depend. These factors are the length and size of their surfaces and edges as well as their face angles. The shape is named after their geometry. The main seven types of crystals are as follows:

• Cubic
• Orthorhombic
• Monoclinic
• Triclinic
• Trigonal
• Hexagonal
• Tetragonal

Answer to Problem 74A

Hexagonal.

Explanation of Solution

The given lengths are as follows:

$\begin{array}{l}a=3\text{ nm}\\ b=\text{3 nm}\\ c=5\text{ nm}\end{array}$

Also, the face angles are as follows:

$\begin{array}{l}\alpha ={90}^{\text{o}}\\ \beta ={90}^{\text{o}}\\ \gamma ={120}^{\text{o}}\end{array}$

The two edge lengths are the same and the third one is more than the other two edge lengths given. Also, two face angles are the same and the other is different. It represents a hexagonal.