*60 The beam from an argon laser (of wavelength 515 nm) has a di-ameter d of 3.00 mm and a continuous energy output rate of 5.00 W.The beam is focused onto a diffuse surface by a lens whose focal lengthfis 3.50 cm. A diffraction pattern such as that of Fig. 36-10 is formed,the radius of the central disk being given by1.22 fAR =(see Eq. 36-12 and Fig. 36-14). The central disk can be shown to con-tain 84% of the incident power. (a) What is the radius of the centraldisk? (b) What is the average intensity (power per unit area) in theincident beam? (c) What is the average intensity in the central disk?

a) The expression for the radius of the central disk is,

Answered: *60 The beam from an argon laser (of…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter27: Wave Optics

Section: Chapter Questions

Problem 12OQ

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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.
Coherent light is passed through two narrow slits whose separation is 20.0 mm. The second-order bright fringe in the interference pattern is located at an angle of 0.0300 rad. If electrons are used instead of light, what must the kinetic energy (in electron volts) of the electrons be if they are to produce an interference pattern for which the second-order maximum is also at 0.0300 rad?
The atoms in a crystal lie in planes separated by a few tenths of a nanometer. Can a crystal be used to produce a diffraction pattern with visible light as it does for x-rays? Explain your answer with reference to Bragg’s law.
Q. 1. An X-ray beam of wavelength 0.71 A is diffracted by a cubic KCL crystal of density 1.99x10^3 Kgm-3. Calculate the interplanner spacing for (200) planes and glancing angle for the second order reflection from these planes. The molecular weight of KCL is 74.6 amu and the Avagadro’s numberis 6.023x10^26 Kg-1 mole-1.
X-rays with a wavelength of 1.43 Å scatter at an angle of 34.0 ∘ from a crystal. If n=1 , what is the distance between planes of atoms in the crystal that give rise to this scattering?
X-rays with wavelengths of 128 pm was used to study a crystal which produced a reflection of 15.8 degrees. Assuming first order diffraction (n = 1), what is the distance between the planes of atoms (d)?
X rays from a copper X- ray tube (A =204 pm) were diffracted at an angle of 35 degrees by a crystal of silicon. Assuming first- order diffraction. Assuming ( n=2 in the bragg equation, what is the interplaner spacing (d) in silicon? (A) 219 pm (B) 217 pm (C) 215 pm (D) 213 pm
If an X-ray beam of wavelength 1.4*10-10 m makes an angle of 20 degrees with a set of planes in a crystal causing first order constructive inference, at what angle will the second order line appear? A) 40 degrees B) 20 degrees C) 43 degrees D) 4.0 degrees E) 11 degrees
X rays of increasing wavelength are reflected from a crystal. Is there a threshold wavelength above which no constructive interference is observed?
Crystal lattices can be examined with x rays but not UV. Why?
Show that Stefan’s law results from Planck’s radiation law. Hin: To compute the total power of blackbody radiation emitted across the entire spectrum of wavelengths at a given temperature, integrate Planck’s law over the entire spectrum P(T)=0I(,T)d. Use the substitution x=hckT and the tabulated value of the integral 0dx x 3( e x 1)=415
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?

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