When an x-ray beam is scattered off the planes of a crystal, the scattered beam creates an interference pattern. This phenomenon is called Bragg scattering. For an observer to measure an interference maximum, two conditions have to be satisfied: 1. The angle of incidence has to be equal to the angle of reflection. 2. The difference in the beam's path from a source to an observer for neighboring planes has to be equal to an integer multiple of the wavelength; that is, 2d sin(0) = mx for m=1,2,.... The path difference 2d sin(0) can be determined from the diagram (Figure 1). The second condition is known as the Bragg condition. Figure 1 of 1 d sine d sine Part A An x-ray beam with wavelength 0.260 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 20.5°. What is the spacing d between the planes of the crystal? Express your answer in nanometers to four significant figures. 15. ΑΣΦ ? d= Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Part B Find the angle 02 at which you will find a second maximum. Express your answer in degrees to three significant figures. [ΠΙ ΑΣΦ ? 0₂ = nm 0

When an x-ray beam is scattered off the planes of a crystal, the scattered beam creates an interference pattern. This phenomenon is called Bragg scattering. For an observer to measure an interference maximum, two conditions have to be satisfied: 1. The angle of incidence has to be equal to the angle of reflection. 2. The difference in the beam's path from a source to an observer for neighboring planes has to be equal to an integer multiple of the wavelength; that is, 2d sin(0) = mx for m=1,2,.... The path difference 2d sin(0) can be determined from the diagram (Figure 1). The second condition is known as the Bragg condition. Figure 1 of 1 d sine d sine Part A An x-ray beam with wavelength 0.260 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 20.5°. What is the spacing d between the planes of the crystal? Express your answer in nanometers to four significant figures. 15. ΑΣΦ ? d= Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Part B Find the angle 02 at which you will find a second maximum. Express your answer in degrees to three significant figures. [ΠΙ ΑΣΦ ? 0₂ = nm 0

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 116AP: Consider a spectrometer based on a diffraction grating. Construct a problem in which you calculate...

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In our study of diffraction by a single slit, we assume that the length of the slit is much larger than the width. What happens to the diffraction pattern if these two dimensions were comparable?
X-rays of wavelength 0.103 nm reflects off a crystal and a second-order maximum is recorded at a Bragg angle of 25.5°. What is the spacing between the scattering planes in this crystal?
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?
Check Your Understanding If the line spacing of a diffraction grating d is not precisely known, we can use a light source with a well-determined wavelength to measure it. Suppose the first-order constructive fringe of the H emission line of hydrogen (=656.3nm) is measured at 11.36° using a spectrometer with a diffraction grating. What is the line spacing of this grating?
What is the distance moved by the traveling mirror of a Michelson interferometer that corresponds to 1500 fringes passing by a point of the observation screen? Assume that the interferometer is illuminated with a 606 nm spectral line of krypton-86.
Check Your Understanding For the experiment in Example 4.2, at what angle from the center is the third maximum and what is its intensity relative to the central maximum?
What are the angular positions of the first and second minima in a diffraction pattern produced by a slit of width 0.20 mm that is illuminated by 400 nm light? What is the angular width of the central peak?
As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change?
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.
Light of wavelength 500 nm falls normally on 50 slits that are 2.5103 mm wide and spaced 5.0103 mm apart. How many interference fringes lie in the central peak of the diffraction pattern?
On a certain crystal, a first-order X-ray diffraction maximum is observed at an angle of 27.1° relative to its surface, using an X-ray source of unknown wavelength. Additionally, when illuminated with a different, this time of known wavelength 0.137 nm, a second-order maximum is detected at 37.3°. Determine (a) the spacing between the reflecting planes, and (b) the unknown wavelength.
(a) Sodium vapor light averaging 589 nm in wavelength falls on a single slit of width 7.50 m. At what angle does it produces its second minimum? (b) What is the highest-order minimum produced?