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Question 1: X-ray Diffraction x-ray diffraction is a method used to identify different types of materials. While this is usually quite a complex process, however for a simple cubic structure, as seen below, we can find the distance between neighboring atoms. The below image shows the diffraction of x-rays passing through a cubic structure and illustrates a change in distance of 2d sine Light rays in phase /IN SA ' ᎾᎥᎾ . 20. b d sin 8 2d sin 0 Atoms in crystal If the wavelength of the x-ray is equal to an integer multiple of this change in distance, we will get constructive interference: mλ = 2d sine 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°. (a) What is the spacing between the scattering planes in this crystal? (b) At what angle will the third-order maximum occur?

Question 1: X-ray Diffraction x-ray diffraction is a method used to identify different types of materials. While this is usually quite a complex process, however for a simple cubic structure, as seen below, we can find the distance between neighboring atoms. The below image shows the diffraction of x-rays passing through a cubic structure and illustrates a change in distance of 2d sine Light rays in phase /IN SA ' ᎾᎥᎾ . 20. b d sin 8 2d sin 0 Atoms in crystal If the wavelength of the x-ray is equal to an integer multiple of this change in distance, we will get constructive interference: mλ = 2d sine 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°. (a) What is the spacing between the scattering planes in this crystal? (b) At what angle will the third-order maximum occur?

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**Question 1: X-ray Diffraction** X-ray diffraction is a method used to identify different types of materials. While this is usually quite a complex process, for a simple cubic structure, as seen below, we can find the distance between neighboring atoms. The image below shows the diffraction of X-rays passing through a cubic structure and illustrates a change in distance of \(2d \sin \theta\). **Diagram Explanation:** The diagram displays X-rays in phase, approaching a crystal. The X-rays are shown interacting with the atoms in the crystal. The geometry highlights the path difference \(2d \sin \theta\) between rays reflecting off different planes. Here, \(d\) is the distance between the planes of atoms, and \(\theta\) is the angle of incidence and reflection. Constructive interference is achieved when this path difference matches an integral multiple of the wavelength (\(m\lambda = 2d \sin \theta\)). **Problem Statement:** X-rays of wavelength 0.103 nm reflect off a crystal, resulting in a second-order maximum recorded at a Bragg angle of 25.5°. (a) What is the spacing between the scattering planes in this crystal? (b) At what angle will the third-order maximum occur?
Transcribed Image Text:**Question 1: X-ray Diffraction** X-ray diffraction is a method used to identify different types of materials. While this is usually quite a complex process, for a simple cubic structure, as seen below, we can find the distance between neighboring atoms. The image below shows the diffraction of X-rays passing through a cubic structure and illustrates a change in distance of \(2d \sin \theta\). **Diagram Explanation:** The diagram displays X-rays in phase, approaching a crystal. The X-rays are shown interacting with the atoms in the crystal. The geometry highlights the path difference \(2d \sin \theta\) between rays reflecting off different planes. Here, \(d\) is the distance between the planes of atoms, and \(\theta\) is the angle of incidence and reflection. Constructive interference is achieved when this path difference matches an integral multiple of the wavelength (\(m\lambda = 2d \sin \theta\)). **Problem Statement:** X-rays of wavelength 0.103 nm reflect off a crystal, resulting in a second-order maximum recorded at a Bragg angle of 25.5°. (a) What is the spacing between the scattering planes in this crystal? (b) At what angle will the third-order maximum occur?
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