Chemistry: Solids and Unit Cells

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Questions and Answers

What is the coordination number for the Body-Centered Cubic (BCC) crystal structure?

8 (correct)

How many total atoms are there in a Body-Centered Cubic (BCC) unit cell?

2 (correct)

What is the atomic packing factor (APF) for the Body-Centered Cubic (BCC) structure?

0.52

0.74

0.68 (correct)

0.78

How many corner atoms contribute to the unit cell in the Hexagonal Close-Packed (HCP) structure?

6 Signup and view all the answers

What additional feature distinguishes the Hexagonal Close-Packed (HCP) structure from cubic structures?

Plane arrangement with three additional atoms in midplane Signup and view all the answers

What is the basic structural unit or building block of the crystal structure called?

Unit cell Signup and view all the answers

Which of the following statements about amorphous solids is true?

They are arranged in an irregular manner Signup and view all the answers

Which unit cell type includes atoms at all eight corners and one atom in the center?

Body-Centered Cubic (BCC) Signup and view all the answers

What is the atomic packing factor characteristic of Face-Centered Cubic (FCC) structures?

0.74 Signup and view all the answers

Which type of crystal structure has a coordination number of 12?

Face-Centered Cubic (FCC) Signup and view all the answers

What type of solid is Polonium classified as based on its crystal structure?

Simple cubic element Signup and view all the answers

How are atoms arranged in a Simple Cubic (SC) crystal structure?

At corners only Signup and view all the answers

Which of the following is NOT a type of cubic unit cell?

Tetragonal Signup and view all the answers

What is the formula to compute the theoretical density of a metallic solid?

$\rho = \frac{n \cdot A}{V_C \cdot N_A}$ Signup and view all the answers

Which of the following types of crystals is characterized by composed charged species?

Ionic Crystals Signup and view all the answers

What is an important consideration when classifying ionic crystals?

The radii of the ions must be known. Signup and view all the answers

How is the edge length of the unit cell in NaCl determined using ionic radii?

It is twice the sum of the ionic radii of Na+ and Cl-. Signup and view all the answers

What is true about the radii of anions and cations in ionic crystals?

Anions are generally larger than cations. Signup and view all the answers

What is the edge length of the unit cell of NaCl as determined experimentally?

564 pm Signup and view all the answers

Which of the following properties of crystals are influenced by the types of forces holding particles together?

Melting point, density, and hardness Signup and view all the answers

What is the value of Avogadro's number?

6.022 x $10^{23}$ atoms/mol Signup and view all the answers

Study Notes

Solids

A solid has a definite shape and volume because its particles are tightly packed.
Solids can exist as crystals with regular lattices or as amorphous solids with irregular arrangements.

Unit Cells

Unit cells are the fundamental building blocks of crystal structures.
There are three main types of unit cells: simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC).

Simple Cubic (SC)

The SC unit cell has atoms only at the corners of a cube.
Polonium is the only element with a simple cubic structure.

Face-Centered Cubic (FCC)

FCC unit cells have atoms at each corner and in the center of each face of the cube.
Important characteristics of an FCC structure include a coordination number of 12 and an atomic packing factor of 0.74.
The volume of an FCC unit cell can be calculated using the formula: VC = (4√2)R³
Examples of FCC structures include copper, silver, and gold.

Atomic Packing Factor

The atomic packing factor represents the proportion of space occupied by atoms in a unit cell.
It is calculated by dividing the volume of atoms in the unit cell by the volume of the unit cell.
A higher atomic packing factor indicates a more efficient packing of atoms.

Body-Centered Cubic (BCC)

BCC unit cells have atoms at each corner and one atom at the center of the cube.
Important characteristics of a BCC structure include a coordination number of 8 and an atomic packing factor of 0.68.
The edge length (a) of a BCC unit cell is related to the atomic radius (R) by the equation: a = 4R/√3.
Examples of BCC structures include iron, chromium, and tungsten.

Hexagonal Close-Packed (HCP)

HCP unit cells have atoms at the corners of a hexagon, a single atom in the center of the hexagon, and three atoms between the top and bottom planes.
Important characteristics of an HCP structure include a coordination number of 12 and an atomic packing factor of 0.74.
The number of atoms per unit cell in an HCP structure can be calculated using the equation: N = (12 * 1/6) + 2 + 3 = 6.
Examples of HCP structures include magnesium, zinc, and titanium.

Density Computations

The theoretical density of a solid can be calculated using the equation: ρ = (n * A) / (VC * NA).
Where:
- n = number of atoms per unit cell
- A = atomic weight
- VC = volume of the unit cell
- NA = Avogadro’s number (6.022 x 10^23 atoms/mol)

Types of Crystals

Crystals are classified into four types based on the forces holding the particles together: ionic, covalent, molecular, and metallic.

Ionic Crystals

Ionic crystals are composed of charged species (anions and cations).
Anions and cations in ionic crystals are generally quite different in size, and their radii need to be considered for understanding the structure and stability of the compound.
The edge length of an ionic crystal unit cell is often related to the sum of the ionic radii.
Examples of ionic crystals include NaCl (sodium chloride), CaCl2 (calcium chloride), and MgO (magnesium oxide).

Conclusion

Understanding the basic concepts of crystal structures, unit cells, density computations, and different crystal types is crucial in the study of engineering materials.
These concepts provide insights into the properties and behaviors of materials used in various engineering applications.

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Description

Explore the unique properties of solids and their structures with this quiz. Learn about different types of unit cells, including simple cubic and face-centered cubic, along with their characteristics and examples. Test your knowledge of atomic packing factors and crystal arrangements.