Textbook Question
An element crystallizes in a face-centered cubic lattice. The edge of the unit cell is 4.078 Å, and the density of the crystal is 19.30 g>cm3. Calculate the atomic weight of the element and identify the element.
1519
views
1
rank
Ch.12 - Solids and Modern Materials
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement140
- Ch.2 - Atoms, Molecules, and Ions192
- Ch.3 - Chemical Reactions and Reaction Stoichiometry172
- Ch.4 - Reactions in Aqueous Solution156
- Ch.5 - Thermochemistry151
- Ch.6 - Electronic Structure of Atoms137
- Ch.7 - Periodic Properties of the Elements127
- Ch.8 - Basic Concepts of Chemical Bonding143
- Ch.9 - Molecular Geometry and Bonding Theories167
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces97
- Ch.12 - Solids and Modern Materials129
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics175
- Ch.15 - Chemical Equilibrium107
- Ch.16 - Acid-Base Equilibria127
- Ch.17 - Additional Aspects of Aqueous Equilibria133
- Ch.18 - Chemistry of the Environment88
- Ch.19 - Chemical Thermodynamics140
- Ch.20 - Electrochemistry137
- Ch.21 - Nuclear Chemistry99
- Ch.22 - Chemistry of the Nonmetals66
- Ch.23 - Transition Metals and Coordination Chemistry69
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry11
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
Chapter 12, Problem 36a
Calcium crystallizes in a body-centered cubic structure at 467°C. (a) How many Ca atoms are contained in each unit cell?
Verified step by step guidance1
Understand the structure: A body-centered cubic (BCC) structure has atoms at each corner of the cube and one atom in the center of the cube.
Calculate the contribution of corner atoms: Each corner atom is shared by 8 adjacent unit cells, so each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
Calculate the total contribution from corner atoms: Since there are 8 corners in a cube, the total contribution from corner atoms is \( 8 \times \frac{1}{8} = 1 \) atom.
Consider the center atom: In a BCC structure, there is one whole atom located at the center of the cube, contributing fully to the unit cell.
Add the contributions: The total number of Ca atoms in a BCC unit cell is the sum of the corner atoms and the center atom, which is \( 1 + 1 = 2 \) atoms.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Body-Centered Cubic (BCC) Structure
The body-centered cubic (BCC) structure is a type of crystal lattice where atoms are located at each of the eight corners of a cube and a single atom is positioned at the center of the cube. This arrangement results in a coordination number of 8, meaning each atom is in contact with eight neighboring atoms. Understanding this structure is essential for determining the number of atoms per unit cell.
Unit Cell
A unit cell is the smallest repeating unit in a crystal lattice that reflects the symmetry and structure of the entire crystal. It defines the arrangement of atoms in the crystal and is characterized by its dimensions and angles. In the case of BCC, the unit cell contains a specific number of atoms that can be calculated based on the arrangement of atoms within the cell.
Atomic Packing Factor (APF)
The atomic packing factor (APF) is a measure of how efficiently atoms are packed in a unit cell. It is calculated as the ratio of the volume occupied by the atoms in the unit cell to the total volume of the unit cell. For BCC structures, the APF is approximately 0.68, indicating that 68% of the volume is filled with atoms, which helps in understanding the density and stability of the crystal structure.
Recommended video:
Guided course
01:56
Conversion Factors