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Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437

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BuyFindarrow_forward

Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437
Chapter 21, Problem 21.24E
Textbook Problem
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Although first-order diffractions might occur at angles greater than 30 ° , if they do there will not be a second-order (or higher) diffraction. Use Bragg’s law to argue why this is the case. (Consider the properties of the sine function at angles greater that 30 ° .)

Interpretation Introduction

Interpretation:

The reason as to why there would not be second-order diffraction if the first-order diffractions occur at angles greater than 30° is to be explained.

Concept introduction:

A unit cell of the crystal is the three-dimensional arrangement of the atoms present in the crystal. The unit cell is the smallest and simplest unit of the crystal which on repetition forms an entire crystal. The parameters of a crystal can be obtained experimentally by X-ray diffraction technique.

Explanation of Solution

The Bragg equation for diffraction of X rays is given by an expression as shown below.

nλ=2dsinθ …(1)

Where,

λ is the wavelength of the incident ray.

d is the distance between two parallel planes.

θ is the Bragg’s angle.

n is the order of diffraction.

The value of n for first-order diffractions is 1.

The given Bragg’s angle for first-order diffractions is 30°.

Substitute the value of θ and n in the equation (1).

(1)λ=2dsin30°λ=2d(0.5)λ=d

When Bragg’s angle is greater than 30°, then the above expression will change to λ>d

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Chapter 21 Solutions

Physical Chemistry
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