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 d sine d sine 1 of 1 > Part A An x-ray beam with wavelength 0.160 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 24.0°. What is the spacing d between the planes of the crystal? Express your answer in nanometers to four significant figures. Π| ΑΣΦ d= 0.08757 Submit Previous Answers Request Answer ? X Incorrect; Try Again; 5 attempts remaining ▾ Part B nm Find the angle 02 at which you will find a second maximum. Express your answer in degrees to three significant figures. [ΨΕΙ ΑΣΦ ? O

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 d sine d sine 1 of 1 > Part A An x-ray beam with wavelength 0.160 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 24.0°. What is the spacing d between the planes of the crystal? Express your answer in nanometers to four significant figures. Π| ΑΣΦ d= 0.08757 Submit Previous Answers Request Answer ? X Incorrect; Try Again; 5 attempts remaining ▾ Part B nm Find the angle 02 at which you will find a second maximum. Express your answer in degrees to three significant figures. [ΨΕΙ ΑΣΦ ? O

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 102AP: Radio telescopes are telescopes used for the detection of radio emission from space. Because radio...

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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?
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?
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?
Radio telescopes are telescopes used for the detection of radio emission from space. Because radio waves have much longer wavelengths than visible light, the diameter of a radio telescope must be very large to provide good resolution. For example, the radio telescope in Penticton, BC in Canada, has a diameter of 26 m and can be operated at frequencies as high as 6.6 GHz. (a) What is the wavelength corresponding to this frequency? (b) What is the angular separation of two radio sources that can be resolved by this telescope? (c) Compare the telescope’s resolution with the angular size of the moon.
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?
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.
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.
A first-order Bragg reflection maximum is observed when a monochromatic X-ray falls on a crystal at a 32.3° angle to a reflecting plane. What is the wavelength of this X-ray?
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?
A telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The laser beam is sent through the telescope in opposite the normal direction and can then be projected onto a satellite or the moon. (a) If this is done with the Mount Wilson telescope, producing a 2.54-m-diameter beam of 633-nm light, what is the minimum angular spread of the beam? (b) Neglecting atmospheric effects, what is the size of the spot this beam would make on the moon, assuming a lunar distance of 3.84108 m?
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.