8.Intensity (relative)40.050.060.070.0Diffraction angle 2080.0Figure 3.25 shows the first four peaks of thex-ray diffraction pattern for copper, which hasan FCC crystal structure; monochromaticx-radiation having a wavelength of 0.1542 nmwas used.(a) Index (i.e., give h, k, and / indices for) eachof these peaks.(b) Determine the interplanar spacing foreach of the peaks.(c) For each peak, determine the atomic ra-dius for Cu and compare these with the valuepresented in Table 3.1.90.0Figure 3.25 Diffractionpattern for polycrystallinecopper. Table 3.1 Atomic Radii and Crystal Structures for 16 MetalsAtomicRadius(nm)MetalAluminumCadmiumChromiumCobaltCopperGoldIron (a)LeadCrystalStructureFCCHCPBCCHCPFCCFCCBCCFCC0.14310.14900.12490.12530.12780.14420.12410.1750MetalMolybdenumNickelPlatinumSilverTantalumTitanium (a)TungstenZincCrystalStructureBCCFCCFCCFCCBCCHCPBCCHCPAtomicRadius(nm)0.13630.12460.13870.14450.14300.14450.13710.1332"FCC = face-centered cubic; HCP = hexagonal close-packed; BCC = body-centered cubic.A nanometer (nm) equals 10-9 m; to convert from nanometers to angstrom units (Å),multiply the nanometer value by 10.

The objective of the question is to find the index, interplanar distance, and atomic radius for each…

Intensity (relative) 40.0 50.0 70.0 Diffraction angle 20 60.0 80.0 Figure 3.25 shows the first four peaks of the x-ray diffraction pattern for copper, which has an FCC crystal structure; monochromatic x-radiation having a wavelength of 0.1542 nm was used. (a) Index (i.e., give h, k, and / indices for) each of these peaks. (b) Determine the interplanar spacing for each of the peaks. (c) For each peak, determine the atomic ra- dius for Cu and compare these with the value presented in Table 3.1. 90.0 Figure 3.25 Diffraction pattern for polycrystalline copper.

Intensity (relative) 40.0 50.0 70.0 Diffraction angle 20 60.0 80.0 Figure 3.25 shows the first four peaks of the x-ray diffraction pattern for copper, which has an FCC crystal structure; monochromatic x-radiation having a wavelength of 0.1542 nm was used. (a) Index (i.e., give h, k, and / indices for) each of these peaks. (b) Determine the interplanar spacing for each of the peaks. (c) For each peak, determine the atomic ra- dius for Cu and compare these with the value presented in Table 3.1. 90.0 Figure 3.25 Diffraction pattern for polycrystalline copper.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

8.
Intensity (relative)
40.0
50.0
60.0
70.0
Diffraction angle 20
80.0
Figure 3.25 shows the first four peaks of the
x-ray diffraction pattern for copper, which has
an FCC crystal structure; monochromatic
x-radiation having a wavelength of 0.1542 nm
was used.
(a) Index (i.e., give h, k, and / indices for) each
of these peaks.
(b) Determine the interplanar spacing for
each of the peaks.
(c) For each peak, determine the atomic ra-
dius for Cu and compare these with the value
presented in Table 3.1.
90.0
Figure 3.25 Diffraction
pattern for polycrystalline
copper.

Table 3.1 Atomic Radii and Crystal Structures for 16 Metals
Atomic
Radius
(nm)
Metal
Aluminum
Cadmium
Chromium
Cobalt
Copper
Gold
Iron (a)
Lead
Crystal
Structure
FCC
HCP
BCC
HCP
FCC
FCC
BCC
FCC
0.1431
0.1490
0.1249
0.1253
0.1278
0.1442
0.1241
0.1750
Metal
Molybdenum
Nickel
Platinum
Silver
Tantalum
Titanium (a)
Tungsten
Zinc
Crystal
Structure
BCC
FCC
FCC
FCC
BCC
HCP
BCC
HCP
Atomic
Radius
(nm)
0.1363
0.1246
0.1387
0.1445
0.1430
0.1445
0.1371
0.1332
"FCC = face-centered cubic; HCP = hexagonal close-packed; BCC = body-centered cubic.
A nanometer (nm) equals 10-9 m; to convert from nanometers to angstrom units (Å),
multiply the nanometer value by 10.

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Step 1: Introduction.

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Step 2: Calculations for the lattice parameter.

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Step 3: Calculations for the interplanar distance (part b).

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Step 4: Calculations for the index (h, k, l) [part a].

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Step 5: Calculations for the atomic radius for each peak.

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