Using X-ray DiffractionWhen an x-ray beam is scattered off the planes of a crystal, the scatteredbeam creates an interference pattern. This phenomenon is called Braggscattering. For an observer to measure an interference maximum, twoconditions have to be satisfied:1. The angle of incidence has to be equal to the angle ofreflection.2. The difference in the beam's path from a source to anobserver for neighboring planes has to be equal to an integermultiple of the wavelength; that is,2d sin(0) = mxfor m = 1, 2, ....The path difference 2d sin(0) can be determined from the diagram (Figure 1). The second condition is known as the Bragg condition.Figured sined sine1 of 1Part A—| ΑΣΦd= 0.1339Submit Previous Answers Request AnswerAn x-ray beam with wavelength 0.250 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 21.0°. Whatis the spacing d between the planes of the crystal?Express your answer in nanometers to four significant figures.X Incorrect; Try Again; 4 attempts remainingPart B0₂ =Find the angle 02 at which you will find a second maximum.Express your answer in degrees to three significant figures.ΞΑΣΦSubmit?Request AnswerPart C Complete previous part(s)Provide Feedbacknm?12 of 23OReview | Constants>Next >

Given: Wavelength of x-ray, λ=0.250 nm Angle, θ=21.0° (A) To determine the interplanar spacing for…

When an x-ray beam is scattered off the planes of a crystal, the scattered beam creates an interference pattern. This phenomenon is called Bragg scattering. For an observer to measure an interference maximum, two conditions have to be satisfied: 1. The angle of incidence has to be equal to the angle of reflection. 2. The difference in the beam's path from a source to an observer for neighboring planes has to be equal to an integer multiple of the wavelength; that is, 2d sin(0) = mx for m=1,2,.... The path difference 2d sin(0) can be determined from the diagram ( Figure 1). The second condition is known as the Bragg condition. ▾ ▼ Part A An x-ray beam with wavelength 0.250 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 21.0°. What is the spacing d between the planes of the crystal? Express your answer in nanometers to four significant figures. VT| ΑΣΦ/ 3 d- 0.1339 M ? Submit Previous Answers Request Answer Part B X Incorrect; Try Again; 4 attempts remaining nm Find the angle 82 at which you will find a second maximum. Express your answer in degrees to three significant figures.

When an x-ray beam is scattered off the planes of a crystal, the scattered beam creates an interference pattern. This phenomenon is called Bragg scattering. For an observer to measure an interference maximum, two conditions have to be satisfied: 1. The angle of incidence has to be equal to the angle of reflection. 2. The difference in the beam's path from a source to an observer for neighboring planes has to be equal to an integer multiple of the wavelength; that is, 2d sin(0) = mx for m=1,2,.... The path difference 2d sin(0) can be determined from the diagram ( Figure 1). The second condition is known as the Bragg condition. ▾ ▼ Part A An x-ray beam with wavelength 0.250 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 21.0°. What is the spacing d between the planes of the crystal? Express your answer in nanometers to four significant figures. VT| ΑΣΦ/ 3 d- 0.1339 M ? Submit Previous Answers Request Answer Part B X Incorrect; Try Again; 4 attempts remaining nm Find the angle 82 at which you will find a second maximum. Express your answer in degrees to three significant figures.

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 102AP: Radio telescopes are telescopes used for the detection of radio emission from space. Because radio...

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X-rays of wavelength 0.103 nm reflects off a crystal and a second-order maximum is recorded at a Bragg angle of 25.5°. What is the spacing between the scattering planes in this crystal?
Radio telescopes are telescopes used for the detection of radio emission from space. Because radio waves have much longer wavelengths than visible light, the diameter of a radio telescope must be very large to provide good resolution. For example, the radio telescope in Penticton, BC in Canada, has a diameter of 26 m and can be operated at frequencies as high as 6.6 GHz. (a) What is the wavelength corresponding to this frequency? (b) What is the angular separation of two radio sources that can be resolved by this telescope? (c) Compare the telescope’s resolution with the angular size of the moon.
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.
In each of the following situations, a wave passes through an opening in an absorbing wall. Rank the situations in order from the one in which the wave is best described by the ray approximation to the one ill which the wave coming through the opening spreads out most nearly equally in all directions in the hemisphere beyond the wall, (a) The sound of a low whistle at 1 kHz passes through a doorway 1 m wide, (b) Red light passes through the pupil of your eye. (c) Blue light passes through the pupil of your eye. (d) The wave broadcast by an AM radio station passes through a doorway 1 m wide, (e) An x-ray passes through the space between bones in your elbow Joint.
Light of wavelength 500 nm falls normally on 50 slits that are 2.5103 mm wide and spaced 5.0103 mm apart. How many interference fringes lie in the central peak of the diffraction pattern?
The width of the central peak in a single-slit diffraction pattern is 5.0 mm. The wavelength of the light is 600 nm, and the screen is 2.0 m from the slit. (a) What is the width of the slit? (b) Determine the ratio of the intensity at 4.5 mm from the center of the pattern to the intensity at the center.
A telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The laser beam is sent through the telescope in opposite the normal direction and can then be projected onto a satellite or the moon. (a) If this is done with the Mount Wilson telescope, producing a 2.54-m-diameter beam of 633-nm light, what is the minimum angular spread of the beam? (b) Neglecting atmospheric effects, what is the size of the spot this beam would make on the moon, assuming a lunar distance of 3.84108 m?
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?
The movable mirror of a Michelson interferometer is attached to one end of a thin metal rod of length 23.3 mm. The other end of the rod is anchored so it does not move. As the temperature of the rod changes from 15°C to 25 C , a change of 14 fringes is observed. The light source is a He Ne laser, =632.8 nm . What is the change in length of the metal bar, and what is its thermal expansion coefficient?
To save money on making military aircraft invisible to radar, an inventor decides to coat them with a nonreflective material having an index of refraction of 1.20, which is between that of air and the surface of the plane. This, he reasons, should be much cheaper than designing Stealth bombers. (a) What thickness should the coating be to inhibit the reflection of 4.00-cm wavelength radar? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
Two slits of width 2 m, each in an opaque material, are separated by a center-to-center distance of 6 m. A monochromatic light of wavelength 450 nm is incident on the double-slit. One finds a combined interference and diffraction pattern on the screen. (a) How many peaks of the interference will be observed in the central maximum of the diffraction pattern? (b) How many peaks of the interference will be observed if the slit width is doubled while keeping the distance between the slits same? (c) How many peaks of interference will be observed if the slits are separated by twice the distance, that is, 12 m, while keeping the widths of the slits same? (d) What will happen in (a) if instead of 450-nm light another light of wavelength 680 nm is used? (e) What is the value of the ratio of the intensity of the central peak to the intensity of the next bright peak in (a)? (f) Does this ratio depend on the wavelength of the light? (g) Does this ratio depend on the width or separation of the slits?
The first-order Bragg angle for a certain crystal is 12.1°. What is the second-order angle?