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=. (0) (1) (2) (3) Figure 13 (4) (5) Wy (1) (0) y (2) (3) Figure 14 (a) What is the lattice vector? What is the basis? Specify using the a conventional notation with b==. 4 (b) Monochromatic X-rays of wavelength 2 illuminate the chain. (i) Evaluate the path difference between the waves diffused in the angle 8 by the atom positioned at the origin (0) and the atom placed in position (2). Indicate the possible values of (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 4 factor. a TU (ii) Numerical application: A = 0.5 Å, a = 0.5 Å, determine the table of increasing values from 0, 0≤0≤, for which 2 the diffraction conditions are satisfied. State the values
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=. (0) (1) (2) (3) Figure 13 (4) (5) Wy (1) (0) y (2) (3) Figure 14 (a) What is the lattice vector? What is the basis? Specify using the a conventional notation with b==. 4 (b) Monochromatic X-rays of wavelength 2 illuminate the chain. (i) Evaluate the path difference between the waves diffused in the angle 8 by the atom positioned at the origin (0) and the atom placed in position (2). Indicate the possible values of (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 4 factor. a TU (ii) Numerical application: A = 0.5 Å, a = 0.5 Å, determine the table of increasing values from 0, 0≤0≤, for which 2 the diffraction conditions are satisfied. State the values
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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part b
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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