Chapter 10, Problem 49E

### Chemistry

10th Edition
Steven S. Zumdahl + 2 others
ISBN: 9781305957404

Chapter
Section

### Chemistry

10th Edition
Steven S. Zumdahl + 2 others
ISBN: 9781305957404
Textbook Problem

# X rays from a copper X-ray tube (λ = 154 pm) were diffracted at an angle of 14.22 degrees by a crystal of silicon. Assuming first-order diffraction (n = 1 in the Bragg equation), what is the interplanar spacing in silicon?

Interpretation Introduction

Interpretation:

The interplanar distance of the silicon crystal has to be determined.

Concept introduction:

The structure of a crystalline solid can be determined by X-ray diffraction method using the Bragg equation,

Where,   =2dsinθn=order of diffraction, positive integer.λ=wavelength of  incident light.d =interplanar distance of a crystal.θ=angle of incident light.

Explanation

Explanation

Â Â Â Â Â Â Â Â Â Â Â  Calculate the interplanar distance of the silicon crystal.

Â Â Â Â Â Â Â Â Â Â Â  Given data:Â  Î»â€‰â€‰=â€‰â€‰154â€‰pmâ€‰â€‰=â€‰â€‰154â€‰â€‰Ã—â€‰â€‰10-12â€‰mÎ¸â€‰â€‰=â€‰â€‰â€‰14.22onâ€‰â€‰=â€‰â€‰1â€‰,â€‰firstâ€‰orderâ€‰diffraction

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  nÎ»â€‰â€‰=â€‰â€‰2dâ€‰sinÎ¸1â€‰â€‰Ã—â€‰â€‰154â€‰Ã—â€‰

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