   # X rays of wavelength 2.63 Å were used to analyze a crystal. The angle of first-order diffraction (n = 1 in the Bragg equation) was 15.55 degrees. What is the spacing between crystal planes, and what would be the angle for second-order diffraction (n = 2)? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 9, Problem 50E
Textbook Problem
69 views

## X rays of wavelength 2.63 Å were used to analyze a crystal. The angle of first-order diffraction (n = 1 in the Bragg equation) was 15.55 degrees. What is the spacing between crystal planes, and what would be the angle for second-order diffraction (n = 2)?

Interpretation Introduction

Interpretation:

• The spacing between the planes of a crystal has to be calculated.
• The angle for the second order diffraction has to be determined.

Concept introduction:

X-ray diffraction method is a characteristic method for the structure determination of crystalline solids with high accuracy. This method of experiment operates on the basis of Bragg’s Law, which states,

When X-rays are incident onto the surface of a crystal, the angle of incidence 'θ' , reflects back with the same angle of scattering 'θ' and the path length difference‘d’ is equal to the ‘n’ number of wavelengths.

It can be expressed as,

=2dsinθwhere,n=order of diffraction, positive integer.λ=wavelength of  incident light.=interplanar distance or spacing between the planes of a crystal.θ=angle of incident light.

### Explanation of Solution

Explanation

Calculate the spacing between the planes of a crystal.

given data : λ=2.63×10-10m                   n=1                   θ=15.55o

=2dsinθd=2×sinθ

=1×2.63×10-10m2×sin15.55o=4.91×10-10m=491pm

The given values are substituted for the parameters in the “Bragg equation” and rearranged to obtain the value for spacing between the planes of the crystal‘d’

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
Added sugars can be useful in meeting the high carbohydrate needs of some athletes. T F

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

22-19 Why are all amino acids solids at room temperature?

Introduction to General, Organic and Biochemistry

Why are titanium oxide features visible in the spectra of only the coolest stars?

Horizons: Exploring the Universe (MindTap Course List)

What is the plasma membrane, and what are its main functions?

Biology: The Dynamic Science (MindTap Course List)

Two resistors connected in series have an equivalent resistance of 690 . When they are connected in parallel, t...

Physics for Scientists and Engineers, Technology Update (No access codes included)

Which elements make up about 99% of the mass of living things?

Oceanography: An Invitation To Marine Science, Loose-leaf Versin 