73. 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 Х-ray?

Physics for Scientists and Engineers: Foundations and Connections
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Author:Katz, Debora M.
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Chapter36: Applications Of The Wave Model
Section: Chapter Questions
Problem 63PQ: X-rays incident on a crystal with planes of atoms located 0.378 nm apart produce a diffraction...
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**Question 73**: 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?

In solving this problem, we utilize Bragg's Law, which relates the wavelength of electromagnetic waves to the angle of incidence and the lattice spacing of a crystal. Bragg's Law is given by:

\[ n\lambda = 2d\sin\theta \]

Where:
- \( n \) is the order of reflection (in this case, first-order, so \( n = 1 \)),
- \( \lambda \) is the wavelength of the X-ray,
- \( d \) is the distance between crystal planes,
- \( \theta \) is the angle of incidence (32.3° in this scenario).

By rearranging the formula, we can solve for the wavelength \( \lambda \):

\[ \lambda = \frac{2d\sin\theta}{n} \]

In the given problem, the angle and the order of the reflection are known, but additional information like the distance between crystal planes \( d \) would be required to calculate the exact wavelength. This question is likely intended to facilitate discussion on the application of Bragg’s Law in crystallography.
Transcribed Image Text:**Question 73**: 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? In solving this problem, we utilize Bragg's Law, which relates the wavelength of electromagnetic waves to the angle of incidence and the lattice spacing of a crystal. Bragg's Law is given by: \[ n\lambda = 2d\sin\theta \] Where: - \( n \) is the order of reflection (in this case, first-order, so \( n = 1 \)), - \( \lambda \) is the wavelength of the X-ray, - \( d \) is the distance between crystal planes, - \( \theta \) is the angle of incidence (32.3° in this scenario). By rearranging the formula, we can solve for the wavelength \( \lambda \): \[ \lambda = \frac{2d\sin\theta}{n} \] In the given problem, the angle and the order of the reflection are known, but additional information like the distance between crystal planes \( d \) would be required to calculate the exact wavelength. This question is likely intended to facilitate discussion on the application of Bragg’s Law in crystallography.
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