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?
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
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
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...
Related questions
Question
Please see attached question.
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbae6659a-1034-43de-b5a3-758f1dde940e%2Ff79fb14b-67ea-4b2a-8615-98cfc7cec523%2Fwqrxezr_processed.png&w=3840&q=75)
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.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you

Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning

Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning

College Physics
Physics
ISBN:
9781938168000
Author:
Paul Peter Urone, Roger Hinrichs
Publisher:
OpenStax College

Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning

Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning

College Physics
Physics
ISBN:
9781938168000
Author:
Paul Peter Urone, Roger Hinrichs
Publisher:
OpenStax College

Modern Physics
Physics
ISBN:
9781111794378
Author:
Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:
Cengage Learning

Physics for Scientists and Engineers, Technology …
Physics
ISBN:
9781305116399
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning

College Physics
Physics
ISBN:
9781285737027
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning