### X-ray Diffraction Exercise**Problem Statement:**An X-ray beam of wavelength \( 3.4 \times 10^{-10} \) meters makes an angle of \( 27^\circ \) with a set of planes in a crystal which results in first order constructive interference. Determine the plane spacing in nanometers. (Please include 2 decimal places).**Solution:**To solve this problem, you will need to use Bragg's Law which is represented by the equation:\[ n\lambda = 2d\sin\theta \]where:- \( n \) is the order of the interference (for first order, \( n = 1 \))- \( \lambda \) is the wavelength of the X-ray ( \( 3.4 \times 10^{-10} \) meters)- \( d \) is the distance between the crystal planes- \( \theta \) is the angle of incidence ( \( 27^\circ \) )Rearranging the formula to solve for \( d \):\[ d = \frac{n\lambda}{2\sin\theta} \]Step-by-step calculation:1. Substitute the known values into the equation:\[ d = \frac{(1)(3.4 \times 10^{-10} \, \text{m})}{2\sin(27^\circ)} \]2. Calculate \( \sin(27^\circ) \). Use a calculator to find:\[ \sin(27^\circ) \approx 0.454 \]3. Substitute this value back into the equation:\[ d = \frac{3.4 \times 10^{-10}}{2 \times 0.454} \]4. Perform the division:\[ d \approx \frac{3.4 \times 10^{-10}}{0.908} \approx 3.74 \times 10^{-10} \, \text{m} \]5. Convert the result from meters to nanometers. (1 \, \text{m} = 10^9 \, \text{nm}): \[ d \approx 3.74 \times 10^{-1} \, \text{nm} \]Thus, the plane spacing \( d \) is approximately \( 0.37 \, \text{nm} \).**Conclusion:**The plane spacing is \(

Answered: Image /qna-images/answer/a95228bb-253e-4fe7-850b-62165ba8d3a8.jpg

An X-ray beam of wavelength 3.4 x 10-10 m makes an angle of 27° with a set of planes in a crystal which results in first order constructive interference. Determine the plane spacing in nanometers. (Please include 2 decimal places).

An X-ray beam of wavelength 3.4 x 10-10 m makes an angle of 27° with a set of planes in a crystal which results in first order constructive interference. Determine the plane spacing in nanometers. (Please include 2 decimal places).

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter36: Wave Optics

Section: Chapter Questions

Problem 43AP

See similar textbooks

Similar questions

Integrated Concepts (a) During laser vision correction, at brief burst at 193 nm ultraviolet light is projected onto the cornea of the patient. It makes a spot 1.00 mm in diameter and deposits 0.500 mJ of energy. Calculate the depth of the layer ablated, assuming the corneal tissue has the same properties as water and is initially at 34.0°C. The tissue’s temperature is increased to 100°C and evaporated without further temperature increase. (b) Does your answer imply that the shape of the cornea can be ?nely controlled?
(a) What is the minimum angular spread of a 633-nm wavelength He-Ne laser beam that is originally 1.00 mm in diameter? (b) If this laser is aimed at a mountain cliff 15.0 km away, how big will the illuminated spot be? (c) How big a spot would be illuminated on the Moon, neglecting atmospheric effects? (This might be done to hit a corner reflector to measure the round-trip time and, hence, distance.) Explicitly show how you follow the steps in Problem-Solving Strategies for Wave Optics.
Youngs double-slit experiment underlies the instrument landing system used to guide aircraft to sale landings at some airports when the visibility is pool. Although real systems are more complicated than the example described here, they operate on the same principles. A pilot is trying to align her plane with a runway as suggested in Figure P37.22. Two radio antennas (the black dots in the figure) are positioned adjacent to the runway, separated by d = 40.0 m. The antennas broadcast unmodulated coherent radio waves at .10.0 MHz. The red lines in Figure P37.22 represent paths along which maxima in the interference pattern of the radio waves exist. (a) Find the wavelength of the waves. The pilot locks onto the strong signal radiated along an interference maximum and steers the plane to keep the received signal strong. If she has found the central maximum, the plane will have precisely the correct heading to land when it reaches the runway as exhibited by plane A. (b) What If? Suppose the plane is living along the first side maximum instead as is the case for plane B. How far to the side of the runway centerline will the plane be when it is 2.00 km from the antennas, measured along its direction of travel? (c) It is possible to tell the pilot that she is on the wrong maximum by sending out two signals from each antenna and equipping the aircraft with a two-channel receiver. The ratio of the two frequencies must not be the ratio of small integers (such as 34). Explain how this two-frequency system would work and why it would not necessarily work if the frequencies were related by an integer ratio.
solid state physics 1) If you know that the Bragg angle of reflection from (111) planes in an aluminum crystal is 19.2°. Calculate the distance between these planes, knowing that the wavelength of the X-rays used is 1.54A, and the crystal structure of aluminum is of the face-centered cubic type. 2) Calculate Avogadro's number given that aluminum has a density of 2.7 g/cm and an atomic weight of 27 ?
I Review I Constants I Periodic Table X rays with a wavelength of 0.12 nm undergo first- order diffraction from a crystal at a 61 ° angle of incidence. Part A What is the angle of second-order diffraction? Express your answer using two significant figures. ? 02 = Submit Request Answer
I Review I Constants I Periodic Table X rays with a wavelength of 0.19 nm undergo first- order diffraction from a crystal at a 57 ° angle of incidence. Part A At what angle does first-order diffraction occur for x rays with a wavelen of 0.12 nm ? Express your answer using two significant figures. ΑΣφ ? = Submit Request Answer
Explain the steps to find the answer, which equation you are using and why you are using it. Also a small reflection about the problem. Thanks.
Question-12 An X-ray diffractometer recorder chart for an element that has a cubic crystal structure showed diffraction peaks at the following 20 angles: 40.663°, 47.314°, 69.144°, and 83.448°. Wavelength of the incoming radiation was 0.15405 nm. (a) Determine the crystal structure of the element. (b) Determine the lattice constant of the element. (c) Identify the element1
2 X-Ray Diffraction d sin e to detector incident X-rays Diffraction patterns produced by X-rays can be used to determine the atomic structure of crystals. In a three-dimensional crystal, the diffraction peaks reveal the distance between planes of atoms. In this problem, we consider a one-dimensional crystal: a line of atoms. X-rays with a wavelength of å = 0.15nm are used in a diffraction experiment. The first diffraction peak occurs at an angle of 8.627°. (a) What is the separation between neighboring atoms? (b) At what angles will the next two peaks occur?
7
X-rays of wavelength equal to 0.134 nm give a first order diffraction from the surface of a crystal when the value of 0(theta) is 10.5°. Calculate the distance between the planes in the crystal parallel to the surface examined. Solve correctly please full explanation needed
This question is not part of an exam it is a normal homework question Investigators measure the size of fog droplets using the diffraction of light. A camera records the diffraction pattern on a screen as the droplets pass in front of a laser, and a measurement of the size of the central maximum gives the droplet size. In one test, a 690 nmnm laser creates a pattern on a screen 30 cmcm from the droplets. If the central maximum of the pattern is 0.30 cmcm in diameter, how large is the droplet? Express your answer with the appropriate units.