Chapter 13, Problem 78A

(a)

Interpretation Introduction

Interpretation: Using the figure $13.12$ , the crystal system, which has three uneven edges intersecting at right angles is to be identified.

Concept Introduction: The particles of a crystal are organized in an ordered, repeating, three-dimensional structure. The crystal system is a way of categorizing crystalline compounds based on the unit cell of the substance. There are seven different crystal systems.

Answer to Problem 78A

The three unequal edges intersect at right angles in the orthorhombic crystal system.

Explanation of Solution

The given figures are as follows:

  

From the figure, the cubic, tetragonal, and orthorhombic crystal systems have edges that meet at right angles. Only the orthorhombic crystal system has unequal edges $\left(\text{a}\ne \text{b}\ne \text{c}\right)$ that meet at the right angle $\left(\text{α}=\text{β}=\text{γ}={90}^{\circ }\right)$ . Thus, the orthorhombic crystal system is one in which three unequal edges meet at a right angle.

(b)

Interpretation Introduction

Interpretation: Using the figure $13.12$ , the crystal system, which has three equal edges and three equal but not right angles, is to be identified.

Concept Introduction: The particles of a crystal are organized in an ordered, repeating, three-dimensional structure. The crystal system is a way of categorizing crystalline compounds based on the unit cell of the substance. There are seven different crystal systems.

Answer to Problem 78A

No crystal system has three equal edges and three equal but not right angles.

Explanation of Solution

The given figures are as follows:

  

From the figure, the cubic, tetragonal, and orthorhombic crystal systems have edges that meet at right angles. Thus, no crystal system which shows three equal edges and three equal but not right angles.

(c)

Interpretation Introduction

Interpretation: Using the figure $13.12$ , the crystal system with three edges, two equal and one uneven, intersect at right angles is to be identified.

Concept Introduction: The particles of a crystal are organized in an ordered, repeating, three-dimensional structure. The crystal system is a way of categorizing crystalline compounds based on the unit cell of the substance. There are seven different crystal systems.

Answer to Problem 78A

In the tetragonal crystal system, three edges, two equal and one unequal meet at right angles.

Explanation of Solution

The given figures are as follows:

  

From the figure, the cubic, tetragonal, and orthorhombic crystal systems have edges that meet at right angles. Only the tetragonal crystal system has two equal edges, and one unequal edge $\left(\text{a}=\text{b}\ne \text{c}\right)$ , which meets at the right angle $\left(\text{α}=\text{β}=\text{γ}={90}^{\circ }\right)$ . Thus, the tetragonal crystal system is one in which two equal edges and one unequal edge meet at right angles.

(d)

Interpretation Introduction

Interpretation: Using the figure $13.12$ , the crystal system, which has three uneven edges that do not intersect at right angles is to be identified.

Concept Introduction: The particles of a crystal are organized in an ordered, repeating, three-dimensional structure. The crystal system is a way of categorizing crystalline compounds based on the unit cell of the substance. There are seven different crystal systems.

Answer to Problem 78A

No crystal system has three unequal edges that do not intersect at right angles.

Explanation of Solution

The given figures are as follows:

  

From the figure, the cubic, tetragonal, and orthorhombic crystal systems have edges that meet at right angles. Thus, no crystal system shows three uneven edges that do not meet at right angles.

(e)

Interpretation Introduction

Interpretation: Using the figure $13.12$ , the crystal system which has three equal edges and these edges intersect at right angles is to be identified.

Concept Introduction: The particles of a crystal are organized in an ordered, repeating, three-dimensional structure. The crystal system is a way of categorizing crystalline compounds based on the unit cell of the substance. There are seven different crystal systems.

Answer to Problem 78A

Three equal edges in the cubic crystal system meet at the right angles.

Explanation of Solution

The given figures are as follows:

  

From the figure, the cubic, tetragonal, and orthorhombic crystal systems have edges that meet at right angles. Only the cubic crystal system has equal edges $\left(\text{a}=\text{b}=\text{c}\right)$ and meets at the right angle $\left(\text{α}=\text{β}=\text{γ}={90}^{\circ }\right)$ . Thus, the cubic crystal system is one in which three equal edges meet at right angles.