Chapter 12, Problem 12.9QAP

Interpretation Introduction

(a)

Interpretation:

The goniometer setting to observe the ka₁ lines for Fe (1.76 $\stackrel{\text{0}}{\text{A}}$ ), Se (0.992 $\stackrel{\text{0}}{\text{A}}$ ) and Ag (0.497 $\stackrel{\text{0}}{\text{A}}$ ) needs to be determined if the diffracting crystal is a topaz.

Concept introduction:

Bragg’s diffraction condition will be used for the calculation of goniometer setting. This formula is given as-

$n\lambda =2d\sin \theta$

Where,

n = integer

λ= wavelength

d = interplanar distance of crystal

θ= angle

Answer to Problem 12.9QAP

Value of Goniometer setting in terms of 2θ when crystal is topaz-

For Fe = 80.9°

For Se = 42.9°

For Ag = 20.9°

Explanation of Solution

Mathematical expression for the Bragg’s diffraction condition is given below -

$n\lambda =2d\sin \theta$     …… (1)

Goniometer setting value in terms of 2θ when a diffracting crystal is a topaz-

Value of d for topaz = 1.356 $\stackrel{\text{0}}{\text{A}}$

The wavelength of ka₁ lines for Fe = 1.76 $\stackrel{\text{0}}{\text{A}}$

n =1

Put this value in equation (1):

$1\times 1.76=2\times 1.356\times \sin \theta$

$\sin \theta =0.648$

$\theta ={\sin }^{-1}(0.922)=40.46°$

$2\theta =80.9°$ for Fe

Wavelength of ka₁ lines for Se = 0.992 $\stackrel{\text{0}}{\text{A}}$

n =1

Put this value in equation (1)

$1\times 0.992=2\times 1.356\times \sin \theta$

$\sin \theta =0.365$

$\theta ={\sin }^{-1}(0.365)=21.45°$

$2\theta =42.9°$ for Se

Wavelength of ka₁ lines for Ag = 0.497 $\stackrel{0}{A}$

n =1

Put this value in equation (1)-

$1\times 0.497=2\times 1.356\times \sin \theta$

$\sin \theta =0.181$

$\theta ={\sin }^{-1}(0.181)=10.45°$

$2\theta =20.9°$ for Ag

Interpretation Introduction

(b)

Interpretation:

The goniometer setting to observe the ka₁ lines for Fe (1.76 $\stackrel{\text{0}}{\text{A}}$ ), Se (0.992 $\stackrel{\text{0}}{\text{A}}$ ) and Ag (0.497 $\stackrel{\text{0}}{\text{A}}$ ) needs to be determined if the diffracting crystal is LiF.

Concept introduction:

Bragg’s diffraction condition will be used for the calculation of goniometer setting. This formula is given as-

$n\lambda =2d\sin \theta$

Where,

n = integer

λ= wavelength

d = interplanar distance of crystal

θ= angle

Answer to Problem 12.9QAP

Value of goniometer setting in terms of 2θ when crystal is LiF-

For Fe = 51.8°

For Se = 28.4°

For Ag = 14.02°

Explanation of Solution

Formula is given below- $n\lambda =2d\sin \theta$     … (1)

Goniometer setting value in terms of 2θ when diffracting crystal is LiF-

Value of d for LiF = 2.014 $\stackrel{\text{0}}{\text{A}}$

Wavelength of ka₁ lines for Fe = 1.76 $\stackrel{\text{0}}{\text{A}}$

n =1

Put this value in equation (1)-

$1\times 2.014=2\times 1.356\times \sin \theta$

$\sin \theta =0.436$

$\theta ={\sin }^{-1}(0.436)=25.90°$

$2\theta =51.8°$ for Fe

Wavelength of ka₁ lines for Se = 0.992 $\stackrel{\text{0}}{\text{A}}$

n =1

Put this value in equation (1)-

$1\times 2.014=2\times 1.356\times \sin \theta$

$\sin \theta =0.246$

$\theta ={\sin }^{-1}(0.365)=14.25°$

$2\theta =28.5°$ for Se

Wavelength of ka₁ lines for Ag = 0.497 $\stackrel{\text{0}}{\text{A}}$

n =1

Put this value in equation (1)-

$1\times 2.014=2\times 1.356\times \sin \theta$

$\sin \theta =0.122$

$\theta ={\sin }^{-1}(0.122)=7.01°$

$2\theta =14.02°$ for Ag

Interpretation Introduction

(c)

Interpretation:

The goniometer setting to observe the ka₁ lines for Fe (1.76 $\stackrel{\text{0}}{\text{A}}$ ), Se (0.992 $\stackrel{\text{0}}{\text{A}}$ ) and Ag (0.497 $\stackrel{\text{0}}{\text{A}}$ ) needs to be determined if the diffracting crystal is NaCl.

Concept introduction:

Bragg’s diffraction condition will be used for the calculation of goniometer setting. This formula is given as-

$n\lambda =2d\sin \theta$

Where,

n = integer

λ= wavelength

d = interplanar distance of crystal

θ= angle

Answer to Problem 12.9QAP

Value of Goniometer setting in terms of 2θ when a crystal is NaCl-

For Fe = 36.4°

For Se = 20.3°

For Ag = 10.00°

Explanation of Solution

The formula is given below- $n\lambda =2d\sin \theta$     … (1)

Goniometer setting value in terms of 2θ when a diffracting crystal is NaCl-

Value of d for NaCl = 2.820 $\stackrel{\text{0}}{\text{A}}$

The wavelength of ka₁ lines for Fe = 1.76 $\stackrel{\text{0}}{\text{A}}$

n =1

Put this value in equation (1)-

$1\times 2.820=2\times 1.356\times \sin \theta$

$\sin \theta =0.32$

$\theta ={\sin }^{-1}(0.32)=18.18°$

$2\theta =36.4°$ for Fe

Wavelength of ka₁ lines for Se = 0.992 $\stackrel{\text{0}}{\text{A}}$

n =1

Put this value in equation (1)-

$1\times 2.820=2\times 1.356\times \sin \theta$

$\sin \theta =0.175$

$\theta ={\sin }^{-1}(0.175)=10.13°$

$2\theta =20.3°$ for Se

Wavelength of ka₁ lines for Ag = 0.497 $\stackrel{\text{0}}{\text{A}}$

n =1

Put this value in equation (1)-

$1\times 2.820=2\times 1.356\times \sin \theta$

$\sin \theta =0.087$

$\theta ={\sin }^{-1}(0.087)=5.00°$

$2\theta =10.00°$ for Ag