Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Textbook Question
Chapter 36, Problem 69P
X rays of wavelength 0.12 nm are found to undergo second-order reflection at a Bragg angle of 28° from a lithium fluoride crystal. What is the interplanar spacing of the reflecting planes in the crystal?
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X rays of wavelength 0.12 nm are found to undergo secondorder reflection at a Bragg angle of 28° from a lithium fluoride crystal.What is the interplanar spacing of the reflecting planes in the crystal?
A parallel X-ray beam is diffracted by sodium chloride. Strong first-order is obtained when the Bragg angle (the angle between the crystal planes and the emerging beam) is 6º 50’. The distance between the planes that are in the reflection position in the crystal is 2,8 Å. 1 angstron = 1 Å = 0,1 nm.
a) What is the wavelength of X-rays?
The structure of the NaCl crystal forms reflecting planes 0.541 nm apart. An X-ray diffraction experiment reflects 0.105 nm X-rays off of a NaCl crystal.
What is the smallest angle, as measured from the reflecting planes in degrees, at which X-ray diffraction may be observed?
Chapter 36 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 36 - You are conducting a single-slit diffraction...Ch. 36 - In a single-slit diffraction experiment, the top...Ch. 36 - For three experiments, Fig. 36-30 gives the...Ch. 36 - For three experiments, Fig. 36-31 gives versus...Ch. 36 - Figure 36-32 shows four choices for the...Ch. 36 - Prob. 6QCh. 36 - At night many people see rings called entoptic...Ch. 36 - a For a given diffraction grating, does the...Ch. 36 - Figure 36-33 shows a red line and a green line of...Ch. 36 - For the situation of Question 9 and Fig. 36-33, if...
Ch. 36 - a Figure 36-34a shows the lines produced by...Ch. 36 - Figure 36-35 shows the bright fringes that lie...Ch. 36 - In three arrangements you view two closely spaced...Ch. 36 - For a certain diffraction grating, the ratio /a of...Ch. 36 - GO The distance between the first and fifth minima...Ch. 36 - What must be the ratio of the slit width to the...Ch. 36 - A plane wave of wavelength 590 nm is incident on a...Ch. 36 - In conventional television, signals are broadcast...Ch. 36 - A single slit is illuminated by light of...Ch. 36 - Monochromatic light of wavelength 441 nm is...Ch. 36 - Light of wavelength 633 nm is incident on a narrow...Ch. 36 - Sound waves with frequency 3000 Hz and speed 343...Ch. 36 - SSM ILW A slit 1.00 mm wide is illuminated by...Ch. 36 - GO Manufacturers of wire and other objects of...Ch. 36 - A 0.10-mm-wide slit is illuminated by light of...Ch. 36 - Figure 36-38 gives versus the sine of the angle ...Ch. 36 - Monochromatic light with wavelength 538 nm is...Ch. 36 - In the single-slit diffraction experiment of Fig....Ch. 36 - SSM WWW The full width at half-maximum FWHM of a...Ch. 36 - Babinets principle. A monochromatic beam of...Ch. 36 - a Show that the values of a at which intensity...Ch. 36 - The wall of a large room is covered with acoustic...Ch. 36 - a How far from grains of red sand must you be to...Ch. 36 - The radar system of a navy cruiser transmits at a...Ch. 36 - SSM WWW Estimate the linear separation of two...Ch. 36 - Prob. 22PCh. 36 - SSM The two headlights of an approaching...Ch. 36 - Entoptic halos. If someone looks at a bright...Ch. 36 - ILW Find the separation of two points on the Moons...Ch. 36 - The telescopes on some commercial surveillance...Ch. 36 - If Superman really had x-ray vision at 0.10 nm...Ch. 36 - GO The wings of tiger beetles Fig. 36-41 are...Ch. 36 - a What is the angular separation of two stars if...Ch. 36 - GO Floaters. The floaters you see when viewing a...Ch. 36 - SSM Millimeter-wave radar generates a narrower...Ch. 36 - a A circular diaphragm 60 cm in diameter...Ch. 36 - Prob. 33PCh. 36 - Prob. 34PCh. 36 - Suppose that the central diffraction envelope of a...Ch. 36 - A beam of light of a single wavelength is incident...Ch. 36 - In a double-slit experiment, the slit separation d...Ch. 36 - In a certain two-slit interference pattern, 10...Ch. 36 - Light of wavelength 440 nm passes through a double...Ch. 36 - GO Figure 36-45 gives the parameter of Eq. 36-20...Ch. 36 - GO In the two-slit interference experiment of Fig....Ch. 36 - GO a In a double-slit experiment, what largest...Ch. 36 - SSM WWW a How many bright fringes appear between...Ch. 36 - Perhaps to confuse a predator, some tropical...Ch. 36 - A diffraction grating 20.0 mm wide has 6000...Ch. 36 - Visible light is incident perpendicularly on a...Ch. 36 - SSM ILW A grating has 400 lines/mm. How many...Ch. 36 - A diffraction grating is made up of slits of width...Ch. 36 - SSM WWW Light of wavelength 600 nm is incident...Ch. 36 - With light from a gaseous discharge tube incident...Ch. 36 - GO A diffraction grating having 180 lines/mm is...Ch. 36 - GO A beam of light consisting of wavelengths from...Ch. 36 - Prob. 53PCh. 36 - Derive this expression for the intensity pattern...Ch. 36 - SSM ILW A source containing a mixture of hydrogen...Ch. 36 - a How many rulings must a 4.00-cm-wide diffraction...Ch. 36 - Light at wavelength 589 nm from a sodium lamp is...Ch. 36 - A grating has 600 rulings/mm and is 5.0 mm wide. a...Ch. 36 - A diffraction grating with a width of 2.0 cm...Ch. 36 - Prob. 60PCh. 36 - With a particular grating the sodium doublet...Ch. 36 - A diffraction grating illuminated by monochromatic...Ch. 36 - Assume that the limits of the visible spectrum are...Ch. 36 - What is the smallest Bragg angle for x rays of...Ch. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - If first-order reflection occurs in a crystal at...Ch. 36 - X rays of wavelength 0.12 nm are found to undergo...Ch. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Consider a two-dimensional square crystal...Ch. 36 - An astronaut in a space shuttle claims she can...Ch. 36 - SSM Visible light is incident perpendicularly on a...Ch. 36 - A beam of light consists of two wavelengths,...Ch. 36 - SSM In a single-slit diffraction experiment, there...Ch. 36 - GO A double-slit system with individual slit...Ch. 36 - SSM A diffraction grating has resolving power R =...Ch. 36 - The pupil of a persons eye has a diameter of 5.00...Ch. 36 - Prob. 81PCh. 36 - A grating with d = 1.50 m is illuminated at...Ch. 36 - SSM In two-slit interference, if the slit...Ch. 36 - GO In a two-slit interference pattern, what is the...Ch. 36 - A beam of light with a narrow wavelength range...Ch. 36 - If you look at something 40 m from you, what is...Ch. 36 - Two yellow flowers are separated by 60 cm along a...Ch. 36 - In a single-slit diffraction experiment, what must...Ch. 36 - A diffraction grating 3.00 cm wide produces the...Ch. 36 - A single-slit diffraction experiment is set up...Ch. 36 - A diffraction grating has 8900 slits across 1.20...Ch. 36 - In an experiment to monitor the Moons surface with...Ch. 36 - In June 1985, a laser beam was sent out from the...Ch. 36 - A diffraction grating 1.00 cm wide has 10 000...Ch. 36 - SSM If you double the width of a single slit, the...Ch. 36 - When monochromatic light is incident on a slit...Ch. 36 - A spy satellite orbiting at 160 km above Earths...Ch. 36 - Suppose that two points are separated by 2.0 cm....Ch. 36 - A diffraction grating has 200 lines/mm. Light...Ch. 36 - A diffraction grating has 200 rulings/mm, and it...Ch. 36 - Prob. 101PCh. 36 - Monochromatic light wavelength = 450 nm is...Ch. 36 - Light containing a mixture of two wavelengths, 500...Ch. 36 - Prob. 104PCh. 36 - Show that a grating made up of alternately...Ch. 36 - Light of wavelength 500 nm diffracts through a...Ch. 36 - If, in a two-slit interference pattern, there are...Ch. 36 - White light consisting of wavelengths from 400 nm...Ch. 36 - If we make d = a in Fig. 36-50, the two slits...Ch. 36 - Derive Eq. 36-28, the expression for the...Ch. 36 - Prob. 111PCh. 36 - How many orders of the entire visible spectrum...Ch. 36 - An acoustic double-slit system of slit separation...Ch. 36 - Two emission lines have wavelengths and ,...
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- A beam of 580-nm light passes through two closely spaced glass plates at close to normal incidence as shown in Figure P27.23. For what minimum nonzero value of the plate separation d is the transmitted light bright?arrow_forwardThe 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?arrow_forwardX-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?arrow_forward
- 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.arrow_forwardOn 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.arrow_forwardIn the figure, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength 0.820 nm makes an angle θ = 62.3˚ with the top face of the crystal. What is the unit cell size a0?arrow_forward
- let a beam of x rays of wavelength 0.125 nm be incident on an NaCl crystal at angle u 45.0° to the top face of the crystal and a family of reflecting planes. Let the reflecting planes have separation d = 0.252 nm. The crystal is turned through angle f around an axis perpendicular to the plane of the page until these reflecting planes give diffraction maxima. What are the (a) smaller and (b) larger value of f if the crystal is turned clockwise and the (c) smaller and (d) larger value of f if it is turned counterclockwise?arrow_forwardX-rays of wavelength of 1.54 angstroms are used to calculate the spacing of (200) plan in platinum. The Bragg angle for this reflection is 22.4o. What is the side of the unit cell of platinum crystal?arrow_forwardPotassium chloride (KCl) is an ionic solid with a crystalline structure whose planes are 0.314 nm apart. X-rays of wavelength 0.267 nm are used in a Bragg diffraction experiment to study the crystalline structure. At what angle with respect to the atomic planes in the crystal would you expect the first strong reflection to occur?arrow_forward
- You are performing research in an x-ray diffraction laboratory. In one of your experiments, you wish to study x-ray diffraction from a crystal of NaCl using x-rays of wavelength 0.136 nm. (a) For how many angles do you expect to detect a diffraction maximum from the crystal if your x-rays are reflecting from the shaded planes as shown? (b) In another experiment, the crystal is rotated so that the reflections of x-rays arise from parallel planes of sodium and chlorine ions. as shown shows portions of these planes containing atoms within the unit cell. Imagine extending these portions outward to form large planes, one with only sodium ions and the other with only chlorine ions. Considering these planes, for how many angles do you expect to detect a diffraction maximum from the crystal using the same x-rays?arrow_forwardQuartz is a uniaxial birefringent material with ordinary refractive index no = 1.5443 and extraordinary refractive index ne = 1.5534. It is desired to make a thin plate of quartz to convert incidentplane-polarised light of wavelength λ0 = 633 nm into outgoing circular-polarised light.Define the terms ”birefringent” and ”uniaxial”; calculate the required minimum thickness of theplate; and state the required orientation of the no and ne axes relative to the plane of polarisationof the incident light.arrow_forwardAn x-ray beam of a certain wavelength is incident on an NaCl crystal, at 30.0° to a certain family of reflecting planes of spacing 39.8 pm. If the reflection from those planes is of the first order, what is the wavelength of the x rays?arrow_forward
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