Explanation 1) Concept: By using Bragg’s diffraction condition, we can first find the expression for angle between the incoming rays and the reflecting plane. Then we can find the angle ϕ for different conditions. 2) Formula: 2 d sin ⁡ θ = m λ 3) Given: i) λ = 0.125 n m ii) θ = 45.0 ° iii) d = 0.252 n m 4) Calculations: First, we calculate the expression for angle between the incoming rays and the reflecting plane by using Braggs diffraction condition. 2 d sin ⁡ θ ' = m λ sin ⁡ θ ' = m λ 2 d θ ' = s i n - 1 m λ 2 d θ ' = s i n - 1 0.125 m 2 × 0.252 θ ' = sin - 1 ⁡ 0.2480 m … … … … … … … … … … … … … … … … … … … … … … ( 1 ) a) For m = 2 , we get from equation ( 1 ) , θ ' = sin - 1 ⁡ 0.2480 m θ ' = sin - 1 ⁡ 0.2480 × 2 θ ' = 29.7 ° Now the crystal should be turned clockwise; therefore, ϕ = θ - θ ' ϕ = 45 ° - 29

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ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Question

Chapter 36, Problem 71P

To determine

To find:

a) The smaller value of ϕ if the crystal is turned clockwise

b) The larger value of ϕ if the crystal is turned clockwise

c) The smaller value of ϕ if the crystal is turned counter-clockwise

d) The larger value of ϕ if the crystal is turned counter-clockwise

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Chapter 36, Problem 70P

Chapter 36, Problem 72P

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let a beam of x rays of wavelength 0.125 nm be incident on an NaCl crystal at angle u 45.0° to the top face of the crystal and a family of reflecting planes. Let the reflecting planes have separation d = 0.252 nm. The crystal is turned through angle f around an axis perpendicular to the plane of the page until these reflecting planes give diffraction maxima. What are the (a) smaller and (b) larger value of f if the crystal is turned clockwise and the (c) smaller and (d) larger value of f if it is turned counterclockwise?

An x-ray beam of a certain wavelength is incident on an NaCl crystal, at 30.0° to a certain family of reflecting planes of spacing 39.8 pm. If the reflection from those planes is of the first order, what is the wavelength of the x rays?

The angle of a Bragg reflection from a set of crystal planes separated by 128.2 pm is 19.76°. Calculate the wavelength of the X‑rays.

Chapter 36 Solutions

Fundamentals of Physics Extended

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a) The smaller value of ϕ if the crystal is turned clockwise b) The larger value of ϕ if the crystal is turned clockwise c) The smaller value of ϕ if the crystal is turned counter-clockwise d) The larger value of ϕ if the crystal is turned counter-clockwise

Concept explainers

To find: a) The smaller value of ϕ if the crystal is turned clockwise b) The larger value of ϕ if the crystal is turned clockwise c) The smaller value of ϕ if the crystal is turned counter-clockwise d) The larger value of ϕ if the crystal is turned counter-clockwise

Want to see the full answer?

Chapter 36 Solutions

To find:

a) The smaller value of ϕ if the crystal is turned clockwise

b) The larger value of ϕ if the crystal is turned clockwise

c) The smaller value of ϕ if the crystal is turned counter-clockwise

d) The larger value of ϕ if the crystal is turned counter-clockwise