Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Question
Chapter 21, Problem 21.25E
Interpretation Introduction
Interpretation:
The angle of the first- and second-order diffractions of X- rays having wavelength
Concept introduction:
A unit cell of the crystal is the three-dimensional arrangement of the atoms present in the crystal. The unit cell is the smallest and simplest unit of the crystal which on repetition forms an entire crystal. The parameters of a crystal can be obtained experimentally by X-ray diffraction technique.
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Calculate the first-order (n=1) Bragg diffraction angle for 110.0 pm X-rays passing through a crystalline lattice having a spacing between adjacent molecular layers of 189.0 pm.
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Cesium chloride has a body-centered cubic structure with unit cell 0.4123 nm. What is the potential energy of interaction between the Cs^+ cation and Cl^– anion?
Chapter 21 Solutions
Physical Chemistry
Ch. 21 - Prob. 21.1ECh. 21 - Boron nitride, BN, is a very hard material, harder...Ch. 21 - Prob. 21.3ECh. 21 - Prob. 21.4ECh. 21 - Figure 21.35 shows a unit cell of diamond....Ch. 21 - Prob. 21.6ECh. 21 - How many different unit cells can a crystal have...Ch. 21 - Prob. 21.8ECh. 21 - Prob. 21.9ECh. 21 - Prob. 21.10E
Ch. 21 - Prob. 21.11ECh. 21 - Prob. 21.12ECh. 21 - Prob. 21.13ECh. 21 - Prob. 21.14ECh. 21 - Prob. 21.15ECh. 21 - Prob. 21.16ECh. 21 - Prob. 21.17ECh. 21 - Prob. 21.18ECh. 21 - Prob. 21.19ECh. 21 - Prob. 21.20ECh. 21 - Prob. 21.21ECh. 21 - Prob. 21.22ECh. 21 - Prob. 21.23ECh. 21 - Prob. 21.24ECh. 21 - Prob. 21.25ECh. 21 - Prob. 21.26ECh. 21 - Prob. 21.27ECh. 21 - Prob. 21.28ECh. 21 - For a simple cubic lattice, what is the ratio of...Ch. 21 - Prob. 21.30ECh. 21 - Prob. 21.31ECh. 21 - Consider Figure 21.21. If the lower rightmost...Ch. 21 - Prob. 21.33ECh. 21 - The aluminum-nickel alloy AlNi has a simple cubic...Ch. 21 - Prob. 21.35ECh. 21 - The first two signals from a powdered sample has X...Ch. 21 - Prob. 21.37ECh. 21 - Prob. 21.38ECh. 21 - Prob. 21.39ECh. 21 - Prob. 21.40ECh. 21 - Prob. 21.41ECh. 21 - Prob. 21.42ECh. 21 - Prob. 21.43ECh. 21 - Prob. 21.44ECh. 21 - Prob. 21.45ECh. 21 - What is the coordination number in the cesium...Ch. 21 - Prob. 21.47ECh. 21 - Which solid phase that is, which allotrope of...Ch. 21 - Prob. 21.49ECh. 21 - Prob. 21.50ECh. 21 - Write Born-Haber cycles showing the relationship...Ch. 21 - Prob. 21.52ECh. 21 - Prob. 21.53ECh. 21 - Prob. 21.54ECh. 21 - The lattice energy for potassium iodide, KI, is...Ch. 21 - Prob. 21.56ECh. 21 - Prob. 21.57ECh. 21 - Prob. 21.58ECh. 21 - Prob. 21.59ECh. 21 - Prob. 21.60ECh. 21 - Prob. 21.61ECh. 21 - Prob. 21.62ECh. 21 - Prob. 21.63ECh. 21 - Prob. 21.64E
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- Palladium has a cubic crystal structure in which the edge of the unit cell is 389 pm long. If the density of palladium is 12.02 g/cm3, how many palladium atoms are in a unit cell? In which of the cubic unit cells does palladium crystallize?arrow_forwardA solid is thought to have an orthorhombic structure. Calculate the positions D and 2θ for the plane 111 expected in the diffraction pattern as a result of CuKa radiation(λ=1.54 Å), since the edges of the unit cell are a= 3.50 Å, B=4.0 Å, C=5.5 Å.arrow_forwardThe density of tantalum at 20oC is 16.69 g/cm3 and its unit cell is cubic. Given that the first five observed Bragg diffraction angles are θ =19.31o, 27.88o, 34.95o, 41.41o and 47.69o, find the type of unit cell and its length. Take the wavelength of the x-ray radiation to be λ =154.433 pm.arrow_forward
- The second-order Bragg diffraction of X-rays with l= 1.660 Å from a set of parallel planes in copper occurs at an angle 2Q = 54.70°. Calculate the distance between the scattering planes in the crystal.arrow_forwardPolonium is the only element known to crystallize in the simple cubic lattice. (a) What is the distance between nearest neighbor polo- nium atoms if the first-order diffraction of X-rays with A = 1.785 Å from the parallel faces of its unit cells appears at an angle of 20 = 30.96° from these planes? (b) What is the density of polonium in this crystal (in g cm-3)?arrow_forwardElemental silver (107.8682 amu) reflects X-rays of wavelength 154.18 pm at angles of 19.076°, 22.171°, and 32.256°. However, there are no other reflections at angles less than 33°. Assuming a cubic unit cell, determine its (a) type and (b) dimension (c) Calculate the density of silver.arrow_forward
- Substance Y (107.8682 amu) reflects X-rays of wavelength 154.18 pm at angles of 19.076°, 22.171°, and 32.256°. However, there are no other reflections at angles less than 33°. Assuming a cubic unit cell, determine its (a) typeand (b) dimension. (c) Calculate the density of Yarrow_forwardAn orthorhombic unit cell has dimensions a = 769 pm, b = 891 pm, and c = 690 pm. Calculate the spacing, d, of the {312} planes.arrow_forwarda) It is considered that a solid substance has an orthorhombic structure. Since the edges of the unit cell are a = 3.50Å, b = 4.0 Å, c = 5.5 Å, calculate the d and 2θ positions for the 111 plane expected in the diffraction pattern as a result of CuKα radiation (λ = 1.54 Å). b) What is the Miller index of the plane intersecting the crystal axes (2a, 1b, -3c)?arrow_forward
- A first-order (n = 1) reflection from the plane of a cubic crystal was observed at a glancing angle of 11.2° when Cu Kα X-rays (λ = 154 pm) were used. What is the interatomic distance between the atoms in the unit cell? Answer in pm.arrow_forwardWhat is the value of 0 for the first diffraction line (n = 1) in bcc iron (atomic radius 126 pm) when the X-ray wavelength is 58.0 pm? Hint: Consider the closest set of lattice planes.arrow_forwardCalculate the volume of the hexagonal unit cell of sodium nitrate, for which dimensions are a=1692.9 pm and c=506.96 pmarrow_forward
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