Textbook Question
Diagrams (1) and (2) are energy-level diagrams for two different LEDs. One LED emits red light, and the other emits blue light. Which one emits red, and which blue? Explain.(1) (2)
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Ch.12 - Solids and Solid-State Materials
McMurry8th EditionChemistryISBN: 9781292336145
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Table of contents
- Ch.1 - Chemical Tools: Experimentation & Measurement143
- Ch.2 - Atoms, Molecules & Ions134
- Ch.3 - Mass Relationships in Chemical Reactions149
- Ch.4 - Reactions in Aqueous Solution157
- Ch.5 - Periodicity & Electronic Structure of Atoms92
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory73
- Ch.7 - Covalent Bonding and Electron-Dot Structures47
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure51
- Ch.9 - Thermochemistry: Chemical Energy104
- Ch.10 - Gases: Their Properties & Behavior138
- Ch.11 - Liquids & Phase Changes43
- Ch.12 - Solids and Solid-State Materials56
- Ch.13 - Solutions & Their Properties98
- Ch.14 - Chemical Kinetics79
- Ch.15 - Chemical Equilibrium107
- Ch.16 - Aqueous Equilibria: Acids & Bases94
- Ch.17 - Applications of Aqueous Equilibria125
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium66
- Ch.19 - Electrochemistry130
- Ch.20 - Nuclear Chemistry73
- Ch.21 - Transition Elements and Coordination Chemistry122
- Ch.22 - The Main Group Elements155
- Ch.23 - Organic and Biological Chemistry43
Chapter 12, Problem 20
Titanium oxide crystallizes in the following cubic unit cell: 
(b) What is the formula of titanium oxide?
Verified step by step guidance1
Identify the positions of the titanium (Ti) and oxygen (O) atoms in the unit cell. In the given diagram, the blue spheres represent Zn atoms and the red spheres represent F atoms. For this problem, assume Zn represents Ti and F represents O.
Determine the number of Ti atoms in the unit cell. Ti atoms are located at the corners and the center of each face of the cubic unit cell. Each corner atom is shared by 8 unit cells, and each face-centered atom is shared by 2 unit cells.
Calculate the total contribution of Ti atoms in the unit cell. There are 8 corner atoms, each contributing 1/8 of an atom, and 6 face-centered atoms, each contributing 1/2 of an atom.
Determine the number of O atoms in the unit cell. O atoms are located entirely within the unit cell, so each O atom counts fully.
Calculate the total number of O atoms in the unit cell. There are 4 O atoms inside the unit cell. Combine the contributions of Ti and O atoms to determine the empirical formula of titanium oxide.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Unit Cell Structure
A unit cell is the smallest repeating unit in a crystal lattice that reflects the overall symmetry and structure of the entire crystal. In the case of titanium oxide, understanding the arrangement of atoms within the cubic unit cell is crucial for determining the stoichiometry and formula of the compound. The face-centered cubic structure indicates how atoms are positioned at the corners and the centers of the faces of the cube.
Stoichiometry
Stoichiometry involves the calculation of reactants and products in chemical reactions, based on the conservation of mass. For titanium oxide, knowing the ratio of titanium to oxygen atoms in the unit cell allows us to derive its chemical formula. This concept is essential for understanding how different elements combine in fixed ratios to form compounds.
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Ionic Compounds
Ionic compounds are formed through the electrostatic attraction between positively and negatively charged ions. In the case of titanium oxide, titanium typically forms a cation (Ti^4+) while oxygen forms an anion (O^2-). The balance of these charges is critical in determining the empirical formula, which reflects the simplest whole-number ratio of the constituent ions.
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Related Practice
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Identify each of the following kinds of packing: (d)
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List the four main classes of crystalline solids, and give a specific example of each.
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Identify each of the following kinds of packing: (b)
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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)
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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.
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