Textbook Question
If the band-gap energy of a gallium phosphide (GaP) semiconductor is 222 kJ/mol, calculate the wavelength of light emitted in a GaP light-emitting diode (LED). (LO 12.11) (a) 186 nm (b) 245 nm (c) 539 nm (d) 854 nm
Ch.12 - Solids and Solid-State Materials
McMurry8th EditionChemistryISBN: 9781292336145
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Table of contents
- Ch.1 - Chemical Tools: Experimentation & Measurement170
- Ch.2 - Atoms, Molecules & Ions160
- Ch.3 - Mass Relationships in Chemical Reactions169
- Ch.4 - Reactions in Aqueous Solution199
- Ch.5 - Periodicity & Electronic Structure of Atoms102
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory92
- Ch.7 - Covalent Bonding and Electron-Dot Structures61
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure59
- Ch.9 - Thermochemistry: Chemical Energy122
- Ch.10 - Gases: Their Properties & Behavior155
- Ch.11 - Liquids & Phase Changes54
- Ch.12 - Solids and Solid-State Materials73
- Ch.13 - Solutions & Their Properties120
- Ch.14 - Chemical Kinetics98
- Ch.15 - Chemical Equilibrium125
- Ch.16 - Aqueous Equilibria: Acids & Bases110
- Ch.17 - Applications of Aqueous Equilibria147
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium86
- Ch.19 - Electrochemistry154
- Ch.20 - Nuclear Chemistry96
- Ch.21 - Transition Elements and Coordination Chemistry156
- Ch.22 - The Main Group Elements187
- Ch.23 - Organic and Biological Chemistry51
Chapter 12, Problem 18d
Identify each of the following kinds of packing: (d)
Verified step by step guidance1
Observe the image provided, which shows a unit cell with a red sphere at the center and blue spheres at the corners.
Identify the type of unit cell based on the arrangement of spheres. The red sphere at the center and blue spheres at the corners indicate a specific type of packing.
Recognize that this arrangement is characteristic of a body-centered cubic (BCC) unit cell.
In a BCC unit cell, there is one atom at each corner of the cube and one atom in the center of the cube.
Conclude that the given image represents a body-centered cubic (BCC) packing.
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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 one atom is 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 central atom is surrounded by eight corner atoms. BCC structures are commonly found in metals like iron and chromium, influencing their physical properties.
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Body Centered Cubic Example
Coordination Number
The coordination number refers to the number of nearest neighbor atoms surrounding a central atom in a crystal structure. In the case of the BCC structure, the coordination number is 8, indicating that each atom at the center is in contact with eight corner atoms. This concept is crucial for understanding the packing efficiency and stability of different crystal structures.
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Packing Efficiency
Packing efficiency is a measure of how effectively atoms are packed in a crystal structure, expressed as the ratio of the volume occupied by the atoms to the total volume of the unit cell. In BCC structures, the packing efficiency is approximately 68%, which is lower than that of face-centered cubic (FCC) structures. Understanding packing efficiency helps in predicting the properties of materials, such as density and strength.
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Related Practice
Textbook Question
A superconductor is a material that loses all electrical resistance below a characteristic temperature called the superconducting transitiontemperature. Which graph represents the behavior of a superconductor? (LO 12.13)(a) (b) (c) (d)
Textbook Question
Identify each of the following kinds of packing: (b)
Textbook Question
The following compound undergoes a phase transition from the solid to the smectic liquid crystal phase at 121 °C. Upon further heating, the compound undergoes another transition to liquid phase at 131 °C. (b) Which image represents the arrangement of molecules at 135 °C?
Textbook Question
Titanium oxide crystallizes in the following cubic unit cell: (b) What is the formula of titanium oxide?
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Textbook Question
The following diagrams show the electron populations of the bands of MO energy levels for four different materials: (a) Classify each material as an insulator, a semiconductor, or a conducting metal.