an x-ray beam of wavelengths from 95.0 to 140 pm is incident at u = 45.0° to a family of reflecting planes with spacing d= 275 pm.What are the (a) longest wavelength l and (b) associated order number m and the (c) shortest l and (d) associated m of the intensity maxima in the diffraction of the beam?

an x-ray beam of wavelengths from 95.0 to 140 pm is incident at u = 45.0° to a family of reflecting planes with spacing d= 275 pm.What are the (a) longest wavelength l and (b) associated order number m and the (c) shortest l and (d) associated m of the intensity maxima in the diffraction of the beam?

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 75P: The structure of the NaCl crystal forms reflecting planes 0.541 nm apart. What is the smallest...

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As a single crystal is rotated in an x-ray spectrometer (Fig. 3.22a), many parallel planes of atoms besides AA and BB produce strong diffracted beams. Two such planes are shown in Figure P3.38. (a) Determine geometrically the interplanar spacings d1 and d2 in terms of d0. (b) Find the angles (with respect to the surface plane AA) of the n = 1, 2, and 3 intensity maxima from planes with spacing d1. Let = 0.626 and d0 = 4.00 . Note that a given crystal structure (for example, cubic) has interplanar spacings with characteristic ratios, which produce characteristic diffraction patterns. In this way, measurement of the angular position of diffracted x-rays may be used to infer the crystal structure. Figure P3.38 Atomic planes in a cubic lattice.
The structure of the NaCl crystal forms reflecting planes 0.541 nm apart. What is the smallest angle, measured from these planes, at which X-ray diffraction can be observed, if X-rays of wavelength 0.085 nm are used?
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