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Chemistry: An Atoms First Approach

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

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BuyFindarrow_forward

Chemistry: An Atoms First Approach

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

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Chemistry: An Atoms First Approach
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