Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 3, Problem 45E
(a)
To determine
To Find: The angular full width for visible light.
(b)
To determine
To Find:The Angular full width for x -ray.
(c)
To determine
To Find:The type of wave which is clearly demonstrates a wave nature.
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Nuclear-pumped x-ray lasers are seen as a possible weapon to destroy ICBM booster rockets at ranges up to 2000 km. One limitation on such a device is the spreading of the beam due to diffraction, with resulting dilution of beam intensity. Consider such a laser operating at a wavelength of 1.40 nm. The element that emits light is the end of a wire with diameter 0.200 mm. (a) Calculate the diameter of the central beam at a target 2000 km away from the beam source. (b) What is the ratio of the beam intensity at the target to that at the end of the wire? (The laser is fired from space, so neglect any atmospheric absorption.)
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X rays of wavelength 0.0850 nm are scattered from the atoms of a crystal. The second-order maximum in the Bragg reflection occurs when the angle θ in Fig is 21.5°. What is the spacing between adjacent atomic planes in the crystal?
Chapter 3 Solutions
Modern Physics
Ch. 3 - Prob. 1CQCh. 3 - Prob. 2CQCh. 3 - Prob. 3CQCh. 3 - Prob. 4CQCh. 3 - Prob. 5CQCh. 3 - Prob. 6CQCh. 3 - Prob. 7CQCh. 3 - A ball rebounds elastically from the floor. What...Ch. 3 - Prob. 9CQCh. 3 - Prob. 10CQ
Ch. 3 - Prob. 11ECh. 3 - Prob. 12ECh. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Prob. 16ECh. 3 - Prob. 17ECh. 3 - What is the stopping potential when 250 nm...Ch. 3 - Prob. 19ECh. 3 - Prob. 20ECh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Prob. 23ECh. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - Prob. 27ECh. 3 - Prob. 28ECh. 3 - Prob. 29ECh. 3 - Prob. 30ECh. 3 - Prob. 31ECh. 3 - Prob. 32ECh. 3 - Prob. 33ECh. 3 - Prob. 34ECh. 3 - Prob. 35ECh. 3 - Prob. 36ECh. 3 - Verify that the Chapter 2 formula KE=mc2 applies...Ch. 3 - Prob. 38ECh. 3 - Prob. 39ECh. 3 - Prob. 40ECh. 3 - Prob. 41ECh. 3 - Prob. 42ECh. 3 - Prob. 43ECh. 3 - Prob. 44ECh. 3 - Prob. 45ECh. 3 - Prob. 46ECh. 3 - Prob. 47CECh. 3 - Prob. 49CECh. 3 - Prob. 50CECh. 3 - Prob. 51CECh. 3 - Prob. 52CECh. 3 - Prob. 53CECh. 3 - Prob. 54CECh. 3 - Prob. 55CE
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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?arrow_forwardAs 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_forwardAn electric current through hydrogen gas produces several distinct wavelengths of visible light. What are the wavelengths of the hydrogen spectrum, if they form first-order maxima at angles 24.2°, 25.7°, 29.1°, and 41.0° when projected on a diffraction grating having 10,000 lines per centimeter?arrow_forward
- An X-ray scattering experiment is performed on a crystal whose atoms form planes separated by 0.440 nm. Using an X-ray source of wavelength 0.548 nm, what is the angle (with respect to the planes in question) at which the experimenter needs to illuminate the crystal in order to observe a first-order maximum?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_forwardCheck 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?arrow_forward
- How many helium atoms, each with a radius of about 31 pm, must be placed end to end to have a length equal to one wavelength of 470 nm blue light?arrow_forwardA beam of light with wavelength of 1.00 µm and M2 = 20 is incident on an aperture of 1.5 mm diameter. a) Calculate the divergence angle of the beam in degrees (give the cone full-angle). b) Calculate the diameter of the beam at a distance of 10.00 m away from the aperture in the propagation direction in units of cm. c) It is given that the longitudinal (temporal) coherence length is 70 times the transverse (spatial) coherence length. Calculate the wavelength linewidth of the light in units of pm.aarrow_forwardX-ray beams are reflected from a crystal by Bragg reflection. If the density of the crystal structure is measured with an rms error for 3 parts is 104. The angle the incident and reflected rays make with the crystal plan is 6oand is measured with an rms error of 3.4 minutes of arc. Calculate the rms error in the determination of the X-ray wavelength?arrow_forward
- The first-order diffraction maximum is observed at 12.4° for a crystal having a spacing between planes of atoms of 0.285 nm. (a) What wavelength x-ray is used to observe this first-order pattern? nm (b) How many orders can be observed for this crystal at this wavelength? A leliarrow_forward5 - büt5. Figure below shows the first four peaks of the x-ray diffraction pattern for a typical solid solution, with FCC crystal structure, average atomic weight of 102g/mol and density of 2.84 g/cm3; monochromatic x-radiation having a wavelength of 0.1542 nm was used. (a) For the first peak, determine the approximate atomic radius of atoms in the crystalline structure. (b) Determine the interplanar spacing for each of the peaks. 7000 (111) 6000 5000 (200) 4000 3000 2000 (311) (220) 1000 20 30 40 50 60 70 80 20 (degree) Intensity (CPS)arrow_forwardChapter 36, Problem 031 Millimeter-wave radar generates a narrower beam than conventional microwave radar, making it less vulnerable to antiradar missiles than conventional radar. (a) Calculate the angular width 20 of the central maximum, from first minimum to first minimum, produced by a 220 GHz radar beam emitted by a 53.5-cm-diameter circular antenna. (The frequency is chosen to coincide with a low-absorption atmospheric "window.") (b) What is 20 for a more conventional circular antenna that has a diameter of 1.56 m and emits at a wavelength of 1.6 cm? (a) Number Units (b) Number Unitsarrow_forward
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