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where does this formula come from?

where does this formula come from?

Chemistry
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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where does this formula come from?

Show work neatly and write your answers with appropriate units next to the question. Q1. An x-ray diffractometer recording for an element that has either the BCC or the FCC crystal structure shows diffraction peaks at the following 20 angles: 40, 58, 73, 86.8, 100.4, and 114.7. The wavelength of the x-ray beam used was 0.154 nm. (a) Determine the cubic structure of the element. (b) Determine the lattice constant of the element. (c) Identify the element. Expert Answer (a) Cubic structure of the element S. 20 (deg) e(deg) sin e sin'e No. 1 40 20 0.3420 0.1170 58 29 0.4848 0.2350 3 73 36.5 0.5948 0.3538 4 86.8 43.4 0.6871 0.4721 5 100.4 50.2 0.7683 0.5903 6 114.7 57.35 0.8420 0.7090 Ratio of sin? evalues of the first and second angles (sin'e (sin' e), 0.2350 0.1170 = 0.4979 0.5 %3D For this ratio, the crystal structure corresponds to BCC. If the ratio is 0.75, then the crystal structure is FCC. (b) Lattice constant 2° (n² +k² + °) a? 4 sin? e a = 2 sin' e For BCC crystal structure first set of principal diffracting plane h =1 k=1 1 = 0 sin e = 0.1170 1 = 0.154 nm
Transcribed Image Text:Show work neatly and write your answers with appropriate units next to the question. Q1. An x-ray diffractometer recording for an element that has either the BCC or the FCC crystal structure shows diffraction peaks at the following 20 angles: 40, 58, 73, 86.8, 100.4, and 114.7. The wavelength of the x-ray beam used was 0.154 nm. (a) Determine the cubic structure of the element. (b) Determine the lattice constant of the element. (c) Identify the element. Expert Answer (a) Cubic structure of the element S. 20 (deg) e(deg) sin e sin'e No. 1 40 20 0.3420 0.1170 58 29 0.4848 0.2350 3 73 36.5 0.5948 0.3538 4 86.8 43.4 0.6871 0.4721 5 100.4 50.2 0.7683 0.5903 6 114.7 57.35 0.8420 0.7090 Ratio of sin? evalues of the first and second angles (sin'e (sin' e), 0.2350 0.1170 = 0.4979 0.5 %3D For this ratio, the crystal structure corresponds to BCC. If the ratio is 0.75, then the crystal structure is FCC. (b) Lattice constant 2° (n² +k² + °) a? 4 sin? e a = 2 sin' e For BCC crystal structure first set of principal diffracting plane h =1 k=1 1 = 0 sin e = 0.1170 1 = 0.154 nm
2 (h? +k? +1?) a =- sin'e 0.154 nm (1° +1 +0) 2 0.117 a = 0.3184 nm (c) The lattice constant of tungsten is 0.316 nm which is very close to the given lattice constant. Hence, the element is tungsten.
Transcribed Image Text:2 (h? +k? +1?) a =- sin'e 0.154 nm (1° +1 +0) 2 0.117 a = 0.3184 nm (c) The lattice constant of tungsten is 0.316 nm which is very close to the given lattice constant. Hence, the element is tungsten.
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