Principles of Instrumental Analysis
Principles of Instrumental Analysis
7th Edition
ISBN: 9781337468039
Author: Skoog
Publisher: Cengage
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Chapter 12, Problem 12.9QAP
Interpretation Introduction

(a)

Interpretation:

The goniometer setting to observe the ka1 lines for Fe (1.76 A0 ), Se (0.992 A0 ) and Ag (0.497 A0 ) 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-

nλ=2dsinθ

Where,

n = integer

λ= wavelength

d = interplanar distance of crystal

θ= angle

Expert Solution
Check Mark

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 -

nλ=2dsinθ     …… (1)

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

Value of d for topaz = 1.356 A0

The wavelength of ka1 lines for Fe = 1.76 A0

n =1

Put this value in equation (1):

1×1.76=2×1.356×sinθ

sinθ=0.648

θ=sin1(0.922)=40.46°

2θ=80.9° for Fe

Wavelength of ka1 lines for Se = 0.992 A0

n =1

Put this value in equation (1)

1×0.992=2×1.356×sinθ

sinθ=0.365

θ=sin1(0.365)=21.45°

2θ=42.9° for Se

Wavelength of ka1 lines for Ag = 0.497 A0

n =1

Put this value in equation (1)-

1×0.497=2×1.356×sinθ

sinθ=0.181

θ=sin1(0.181)=10.45°

2θ=20.9° for Ag

Interpretation Introduction

(b)

Interpretation:

The goniometer setting to observe the ka1 lines for Fe (1.76 A0 ), Se (0.992 A0 ) and Ag (0.497 A0 ) 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-

nλ=2dsinθ

Where,

n = integer

λ= wavelength

d = interplanar distance of crystal

θ= angle

Expert Solution
Check Mark

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- nλ=2dsinθ     … (1)

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

Value of d for LiF = 2.014 A0

Wavelength of ka1 lines for Fe = 1.76 A0

n =1

Put this value in equation (1)-

1×2.014=2×1.356×sinθ

sinθ=0.436

θ=sin1(0.436)=25.90°

2θ=51.8° for Fe

Wavelength of ka1 lines for Se = 0.992 A0

n =1

Put this value in equation (1)-

1×2.014=2×1.356×sinθ

sinθ=0.246

θ=sin1(0.365)=14.25°

2θ=28.5° for Se

Wavelength of ka1 lines for Ag = 0.497 A0

n =1

Put this value in equation (1)-

1×2.014=2×1.356×sinθ

sinθ=0.122

θ=sin1(0.122)=7.01°

2θ=14.02° for Ag

Interpretation Introduction

(c)

Interpretation:

The goniometer setting to observe the ka1 lines for Fe (1.76 A0 ), Se (0.992 A0 ) and Ag (0.497 A0 ) 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-

nλ=2dsinθ

Where,

n = integer

λ= wavelength

d = interplanar distance of crystal

θ= angle

Expert Solution
Check Mark

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- nλ=2dsinθ     … (1)

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

Value of d for NaCl = 2.820 A0

The wavelength of ka1 lines for Fe = 1.76 A0

n =1

Put this value in equation (1)-

1×2.820=2×1.356×sinθ

sinθ=0.32

θ=sin1(0.32)=18.18°

2θ=36.4° for Fe

Wavelength of ka1 lines for Se = 0.992 A0

n =1

Put this value in equation (1)-

1×2.820=2×1.356×sinθ

sinθ=0.175

θ=sin1(0.175)=10.13°

2θ=20.3° for Se

Wavelength of ka1 lines for Ag = 0.497 A0

n =1

Put this value in equation (1)-

1×2.820=2×1.356×sinθ

sinθ=0.087

θ=sin1(0.087)=5.00°

2θ=10.00° for Ag

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