Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 3, Problem 11P
To determine
The position of the three brightest red lines on the screen.
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An x-ray was used to examine a sample of chromium having a BCC crystal structure.Using x-rays having a wavelength of 0.1682 nm, a diffractometer is used. The distorting (010) aircraft is the plane. Chromium has an atomic radius of 0.125 nm.
A)Compute the interplanar spacing and Calculate the diffraction angle. Assume second-order of diffraction, n = 2.
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A transmission diffraction grating with 420 lines/mm is used to study the light intensity of different orders (n). A screen is located 2.8 m from the grating. What are the positions on the screen of the three brightest red lines for a hydrogen source?
Chapter 3 Solutions
Modern Physics for Scientists and Engineers
Ch. 3 - Prob. 1QCh. 3 - Prob. 2QCh. 3 - Prob. 3QCh. 3 - Prob. 4QCh. 3 - Prob. 5QCh. 3 - Prob. 6QCh. 3 - Prob. 7QCh. 3 - Prob. 8QCh. 3 - Prob. 9QCh. 3 - In the experiment of Example 3.2, how could you...
Ch. 3 - Prob. 11QCh. 3 - Prob. 12QCh. 3 - Prob. 13QCh. 3 - Prob. 14QCh. 3 - Prob. 15QCh. 3 - Prob. 16QCh. 3 - Prob. 17QCh. 3 - Prob. 18QCh. 3 - Prob. 19QCh. 3 - Prob. 20QCh. 3 - Prob. 21QCh. 3 - Prob. 22QCh. 3 - Prob. 23QCh. 3 - Prob. 24QCh. 3 - Prob. 25QCh. 3 - Prob. 26QCh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Across what potential difference does an electron...Ch. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - Prob. 10PCh. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Prob. 16PCh. 3 - Calculate max for blackbody radiation for (a)...Ch. 3 - Prob. 18PCh. 3 - Prob. 19PCh. 3 - Prob. 20PCh. 3 - White dwarf stars have been observed with a...Ch. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - Prob. 38PCh. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 45PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48PCh. 3 - Prob. 49PCh. 3 - Prob. 50PCh. 3 - Prob. 52PCh. 3 - Prob. 53PCh. 3 - Prob. 54PCh. 3 - Prob. 55PCh. 3 - Prob. 56PCh. 3 - Prob. 57PCh. 3 - Prob. 58PCh. 3 - Prob. 59PCh. 3 - Prob. 60PCh. 3 - Prob. 61PCh. 3 - Prob. 62PCh. 3 - Prob. 63PCh. 3 - Prob. 64PCh. 3 - Prob. 65PCh. 3 - Prob. 66PCh. 3 - Prob. 67PCh. 3 - Prob. 68PCh. 3 - The Fermi Gamma-ray Space Telescope, launched in...Ch. 3 - Prob. 70P
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- X-rays incident on a crystal with planes of atoms located 0.378 nm apart produce a diffraction pattern in which a first-order maximum is observed at an angle of 14.2. a. What is the wavelength of the X-rays incident on the crystal? b. How many orders are visible in the diffraction pattern?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_forwardFor sodium light of wavelength 5893Å, calculate thickness of quarter wave plate. Given ne = 1.553 and no = 1.544.arrow_forward
- The spacing between principal planes in a NaCl crystal is 2.82x10^-10 m. It is found that a first order Bragg reflection of a monochromatic X-ray beam occurs at an angle of 10°. From this information we can say that the wavelength λ of the X-rays and the angle θ2 corresponding to the second-order spectrum are:Choose an answer between the letters A and D from the image below and justify your answerarrow_forwardA diffraction grating with 500 grooves per millimeter is used to study the spectrum of Mercury containing the following lines: violet, blue, green and a yellow doublet. When using the first diffraction grating we notice that we observe the first order of the blue line at an angle of 12.59⁰. a- What is the wavelength blue of the blue line in the spectrum of Mercury? b- At what angles will the green line be observed? We have Agreen = 546.1 nm.s. c- A line is observed at an angle of 23.87°. What is the color of this line? In the following we replace the diffraction grating with another one with unknown spacing. We notice that the first order green line is observed at an angle of 25.91°. d- Find the number of grooves per millimeter for the diffraction grating. e- Find the angular separation of the yellow doublet at first order (2,1 = 579.0 nm and Ay2 = 577.0 nm). f- What resolving power must a grating have to distinguish the yellow doublet?arrow_forwardThe beautiful colors of a blue morpho butterfly are known to be originated from nanoscale structures that function as a natural diffraction grating. Suppose the diffraction grating has 7000 lines/cm, what is the angle of the second-order maximum for 633-nm light? O 20° O 47.2° O 26.3° O 62.4°arrow_forward
- X rays of wavelength 0.0820 nm are scattered from the atoms of a crystal. The second-order maximum in the Bragg reflection occurs when the angle is 20.5°. (Figure 1) For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of X-ray diffraction. Part A What is the spacing between adjacent atomic planes in the crystal? Express your answer in nanometers. ΓΙ ΑΣΦ d = Submit Previous Answers Request Answer ? nmarrow_forwardc) Figure Q3 (c) shows the X-ray diffraction patterns of Aluminum powder by CuK- radiation. i. Sketch the (311) plane in cubic structure using miller indices solution. ii. Calculate the planar spacing, d hkl and angle, 0 hkl for (311) peak if the lattice constant, a is 0.404 nm and I is 0.1542 nm. Note that the diffraction condition is 2dhkl sin 0 = n]. iii. Determine whether the crystal structure of Aluminum powder belongs to bcc or fcc lattices. Justify your answer. (111) 100 A=0.1542 nm (CuK „-radiation) 80 60 (200) 40 (311) (220) 20 (222) (400) (331)(420) 20 30 40 50 60 70 80 90 100 110 120 20 (degrees) Fig. Q3 (c): X-ray diffraction pattern of Aluminum powder by CuK_- radiation. Inte nsity (arbitrary units)arrow_forwarda beam of white light is shined at normal incidence onto the outside of a soap bubble (index of soap solution = 1.340). An observer looking at the bubble, opposite to the direction of the beam, notices that green light (Lambda = 555.0 nm) is particularly bright in the reflected spectrum. What is the second thinnest wall thickness of the bubble?arrow_forward
- 3. A Cu target emits an X-ray line of wavelength = 1.54 Å. a) Given that the Bragg angle for reflection from the (111) planes in Al is 19.2°, compute the interplanar distance for these planes. Recall that aluminum has an fcc structure. b) Knowing that the density and atomic weight of Al are, respectively, 2.7 g/cm3 and 27.0, compute the value of Avogadro's number.arrow_forwardIn an x-ray diffraction experiment, two different samples of DNA of unknown origin are studied. Sample 1 has a layer spacing of Ax = 4nm and the 4th horizontal line as measured from the center of the 'X' is missing (as indicated by the figure below). Sample 2 has a layer spacing of Ax = 1nm and there are no horizontal lines missing from the diffraction pattern. What is a possible explanation for these results? D (diameter) a (rise andgle) B (base stacking) P (helical pitch) S (offset) O The Sample 1 DNA has a smaller pitch P and a smaller offset S than Sample 2 DNA.. The Sample 1 DNA has a smaller pitch P than Sample 2; Sample 1 is a double helix while Sample 2 is a single helix. O The Sample 1 DNA has a larger pitch P than Sample 2; Sample 1 is a double helix while Sample 2 is a single helix. The Sample 1 DNA has a larger pitch P and a smaller offset S than Sample 2 DNA.. O The Sample 1 DNA has a smaller pitch P than Sample 2; Sample 1 is a single helix while Sample 2 is a double…arrow_forwardQ1/ A/ Consider a resonator consisting of two concave spherical mirrors both with radius of curvature 4 m and separated by a distance of 1 m. Calculate the minimum beam diameter of the TEMy mode at the resonator center and on the mirrors when the laser oscillation is Art laser wavelength 2=514.5 nm. Then, Find if this cavity is stable or not. B/ One of the mirrors in A is replaced by a concave mirror of 1.5m radius of curvature, calculate the position of minimum beam radius. Then calculate the beam waist and radius of curvature at 150 cm from M1.arrow_forward
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