In a certain crystal the spacing between crystal planes is 0.165 nm. (a) If you shine a beam of x rays of wavelength 0.124 nm on this crystal, for what angle between the beam and the crystal planes does the first strong interference maximum occur? (b) For what larger angles (if any) do strong interference maxima occur?

In a certain crystal the spacing between crystal planes is 0.165 nm. (a) If you shine a beam of x rays of wavelength 0.124 nm on this crystal, for what angle between the beam and the crystal planes does the first strong interference maximum occur? (b) For what larger angles (if any) do strong interference maxima occur?

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 75P: The structure of the NaCl crystal forms reflecting planes 0.541 nm apart. What is the smallest...

See similar textbooks

Similar questions

Consider a single-slit diffraction pattern for =589 nm, projected on a screen that is 1.00 m from a slit of width 0.25 mm. How far from the center of the pattern are the centers of the first and second dark fringes?
When a monochromatic light of wavelength 430 nm incident on a double slit of slit separation 5 m, there are 11 interference fringes in its central maximum. How many interference fringes will be in the central maximum of a light of wavelength 632.8 nm for the same double slit?
What is the angular width of the central fringe of the interference pattern of (a) 20 slits separated by d=2.0103 mm? (b) 50 slits with the same separation? Assume that =600 nm.
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.
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?
(a) Sodium vapor light averaging 589 nm in wavelength falls on a single slit of width 7.50 m. At what angle does it produces its second minimum? (b) What is the highest-order minimum produced?
Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm.
Both sides of a uniform film that has index of refraction n and thickness d are in contact with air. For normal incidence of light, an intensity minimum is observed in the reflected light at λ2 and an intensity maximum is observed at λ1, where λ1 > λ2. (a) Assuming no intensity minima are observed between λ1 and λ2, find an expression for the integer m in Equations 27.13 and 27.14 in terms of the wavelengths λ1 and λ2. (b) Assuming n = 1.40, λ1 = 500 nm, and λ2 = 370 nm, determine the best estimate for the thickness of the film.
Q1/ 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.
The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (a) Show that the intensity drops to one-half the maximum value when sin2 a = a2/2. (b) Verify that a =1.39 rad (about 80°) is a solution to the transcendental equation of (a). (c) Show that the FWHM is u= 2 sin-1(0.443l/a), where a is the slit width. Calculate the FWHM of the central maximum for slit width (d) 1.00l, (e) 5.00l, and (f) 10.0l.
Coherent electromagnetic waves with wavelength l = 500 nm pass through two identical slits. The width of each slit is a, and the distance between the centers of the slits is d = 9.00 mm. (a) What is the smallest possible width a of the slits if the m = 3 maximum in the interference pattern is not present? (b) What is the next larger value of the slit width for which the m = 3 maximum is absent?
The interplanar distance of (101) plane of ZnO crystal is 0.45 nm. If the first-order diffraction maximum is observed at an incidence angle of 36.2°, what is the wavelength of the X-ray scattering from this crystal? And estimate the crystallite size of the ZnO nanomaterial if FWHM of (101) plane is 2.51° (degree to radian Degree x T/180) and k = 0.9.