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(a) What is the lattice vector? What is the basis? Specify using the conventional notation with b=". 4

(a) What is the lattice vector? What is the basis? Specify using the conventional notation with b=". 4

General Chemistry - Standalone book (MindTap Course List)
General Chemistry - Standalone book (MindTap Course List)
11th Edition
ISBN:9781305580343
Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Chapter23: Organic Chemistry
Section23.2: Alkanes And Cycloalkanes
Problem 23.2CC
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Exercise 15: X-ray diffraction by a row of identical atoms Consider the linear chain of carbon atoms shown in Fig. 13. This structure could easily be a chain of hydrocarbons with alternating single and double bonds such as -C=C-C=C-C=C-C=. a AA (0) (1) (2) (3) (4) (5) (0) (1) (2) (3) Figure 13 Figure 14 (a) What is the lattice vector? What is the basis? Specify using the a conventional notation with b%D 4 (b) Monochromatic X-rays of wavelength 2 illuminate the chain. (i) Evaluate the path difference between the waves diffused in the angle 0 by the atom positioned at the origin (0) and the atom placed in position (2). Indicate the possible values of e (or of one of its trigonometric function) observed by diffraction assuming that the chain consists only of atom pairs (crystal diffraction). Show that the addition of odd atoms accentuates the diffracted intensity in certain directions while diminishing it in others (always assuming that b=). Find the result using the structure a 4 factor. (ii) Numerical application: 1 = 0.5 Å, a = 0.5 Å, determine the table of increasing values from 0, 0<0<", for which the diffraction conditions are satisfied. State the values 2 corresponding to the intensities I/I, in which I, is the diffracted intensity of the group of atoms of the chain and Iç is the diffracted intensity of the atoms only situated at the lattice points.
Transcribed Image Text:Exercise 15: X-ray diffraction by a row of identical atoms Consider the linear chain of carbon atoms shown in Fig. 13. This structure could easily be a chain of hydrocarbons with alternating single and double bonds such as -C=C-C=C-C=C-C=. a AA (0) (1) (2) (3) (4) (5) (0) (1) (2) (3) Figure 13 Figure 14 (a) What is the lattice vector? What is the basis? Specify using the a conventional notation with b%D 4 (b) Monochromatic X-rays of wavelength 2 illuminate the chain. (i) Evaluate the path difference between the waves diffused in the angle 0 by the atom positioned at the origin (0) and the atom placed in position (2). Indicate the possible values of e (or of one of its trigonometric function) observed by diffraction assuming that the chain consists only of atom pairs (crystal diffraction). Show that the addition of odd atoms accentuates the diffracted intensity in certain directions while diminishing it in others (always assuming that b=). Find the result using the structure a 4 factor. (ii) Numerical application: 1 = 0.5 Å, a = 0.5 Å, determine the table of increasing values from 0, 0<0<", for which the diffraction conditions are satisfied. State the values 2 corresponding to the intensities I/I, in which I, is the diffracted intensity of the group of atoms of the chain and Iç is the diffracted intensity of the atoms only situated at the lattice points.
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