Domanda del libro di testo
(a) The density of diamond is 3.5 g/cm3, and that of graphite is 2.3 g/cm3. Based on the structure of buckminsterfullerene, what would you expect its density to be relative to these other forms of carbon?
2396
views
Ch.12 - Solids and Modern Materials
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement177
- Ch.2 - Atoms, Molecules, and Ions231
- Ch.3 - Chemical Reactions and Reaction Stoichiometry216
- Ch.4 - Reactions in Aqueous Solution189
- Ch.5 - Thermochemistry175
- Ch.6 - Electronic Structure of Atoms168
- Ch.7 - Periodic Properties of the Elements150
- Ch.8 - Basic Concepts of Chemical Bonding177
- Ch.9 - Molecular Geometry and Bonding Theories200
- Ch.10 - Gases179
- Ch.11 - Liquids and Intermolecular Forces113
- Ch.12 - Solids and Modern Materials154
- Ch.13 - Properties of Solutions157
- Ch.14 - Chemical Kinetics199
- Ch.15 - Chemical Equilibrium128
- Ch.16 - Acid-Base Equilibria164
- Ch.17 - Additional Aspects of Aqueous Equilibria163
- Ch.18 - Chemistry of the Environment105
- Ch.19 - Chemical Thermodynamics164
- Ch.20 - Electrochemistry171
- Ch.21 - Nuclear Chemistry122
- Ch.22 - Chemistry of the Nonmetals82
- Ch.23 - Transition Metals and Coordination Chemistry79
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry16
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Capitolo 12, Problema 120
In their study of X-ray diffraction, William and Lawrence Bragg determined that the relationship among the wavelength of the radiation 1l2, the angle at which the radiation is diffracted 1u2, and the distance between planes of atoms in the crystal that cause the diffraction (d) is given by nl = 2d sin u. X rays from a copper X-ray tube that have a wavelength of 1.54 Å are diffracted at an angle of 14.22 degrees by crystalline silicon. Using the Bragg equation, calculate the distance between the planes of atoms responsible for diffraction in this crystal, assuming n = 1 (first-order diffraction).
Guida verificata passo dopo passo1
Identify the given values: wavelength (\( \lambda \)) = 1.54 Å, angle (\( \theta \)) = 14.22 degrees, and order of diffraction (n) = 1.
Convert the angle from degrees to radians if necessary, as trigonometric functions typically use radians. However, for this problem, you can use degrees directly in the sine function.
Use the Bragg equation: \( n\lambda = 2d \sin \theta \).
Rearrange the equation to solve for the distance between planes (d): \( d = \frac{n\lambda}{2 \sin \theta} \).
Substitute the known values into the equation: \( d = \frac{1 \times 1.54 \text{ Å}}{2 \sin(14.22^\circ)} \) and calculate the result.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
1mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Bragg's Law
Bragg's Law describes the relationship between the wavelength of X-rays, the angle of diffraction, and the distance between atomic planes in a crystal. It is mathematically expressed as nλ = 2d sin(θ), where n is the order of diffraction, λ is the wavelength, d is the distance between planes, and θ is the angle of diffraction. This law is fundamental in crystallography for determining the structure of crystalline materials.
Video consigliato:
Percorso guidato
02:03
Hess's Law
Wavelength of X-rays
The wavelength of X-rays is a critical parameter in X-ray diffraction studies, influencing how X-rays interact with the crystal lattice. In this context, a wavelength of 1.54 Å (angstroms) is commonly used, particularly for copper X-ray tubes. The wavelength determines the resolution and the ability to distinguish between different atomic planes in the crystal structure.
Video consigliato:
Percorso guidato
00:31Frequency-Wavelength Relationship
Angle of Diffraction
The angle of diffraction (θ) is the angle at which X-rays are scattered by the crystal planes. It is essential for applying Bragg's Law, as it directly affects the calculation of the interplanar spacing (d). In the given problem, the angle of 14.22 degrees is used to find the distance between the planes of atoms, showcasing how the geometry of the crystal influences diffraction patterns.
Video consigliato:
Percorso guidato
01:53Bond Angles
Pratica correlata
Domanda del libro di testo
Germanium has the same structure as silicon, but the unit cell size is different because Ge and Si atoms are not the same size. If you were to repeat the experiment described in the previous problem but replace the Si crystal with a Ge crystal, would you expect the X rays to be diffracted at a larger or smaller angle u?
827
views