Student Solutions Manual for Ball's Physical Chemistry, 2nd
Student Solutions Manual for Ball's Physical Chemistry, 2nd
2nd Edition
ISBN: 9798214169019
Author: David W. Ball
Publisher: Cengage Learning US
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 21, Problem 21.34E

The aluminum-nickel alloy AlNi has a simple cubic lattice with a unit cell parameter of 2.88 A . If X rays having a wavelength of 1.544 A were used, at what angles would the X rays be diffracted by (a) the ( 100 ) plane of atoms; (b) the ( 110 ) plane of atoms; (c) the ( 210 ) plane of atoms?

Expert Solution
Check Mark
Interpretation Introduction

(a)

Interpretation:

The angle by which the X rays would be diffracted by the (100) plane of atoms is to be determined.

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. Unit cell can be a cubic unit cell or hexagonal unit cell. The classification of a unit cell depends on the lattice site occupied by the atoms.

Answer to Problem 21.34E

The angle by which the X rays would be diffracted by the (100) plane of atoms 15.5°.

Explanation of Solution

The d spacing is calculated by formula as shown below.

d=ah2+k2+l2 …(1)

Where,

h,k,lare the Miller indices.

a is the side of the unit cell.

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

nλ=2dsinθ …(2)

Where,

λ is the wavelength of incident ray.

d is the distance between two parallel planes.

θ is the Bragg’s angle.

n is the order of diffraction.

Substitute equation (1) in equation (2).

nλ=2(ah2+k2+l2)sinθsinθ=nλh2+k2+l22a

The above formula can be written as follows:

θ=sin1(nλh2+k2+l22a) …(3)

The given plane is (100). The side of the unit cell is 2.88A. The wavelength of X rays is 1.544A.

Substitute the value of (h,k,l), side and wavelength in equation (3).

θ=sin1(1×1.544A×12+02+022×2.88A)θ=sin10.26805556θ=15.5°

Thus, the angle by which the X rays would be diffracted by the (100) plane of atoms 15.5°.

Conclusion

The angle by which the X rays would be diffracted by the (100) plane of atoms 15.5°.

Expert Solution
Check Mark
Interpretation Introduction

(b)

Interpretation:

The angle by which the X rays would be diffracted by the (110) plane of atoms is to be determined.

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. Unit cell can be a cubic unit cell or hexagonal unit cell. The classification of a unit cell depends on the lattice site occupied by the atoms.

Answer to Problem 21.34E

The angle by which the X rays would be e diffracted by the (110) plane of atoms 22.3°.

Explanation of Solution

The d spacing is calculated by formula as shown below.

d=ah2+k2+l2 …(1)

Where,

h,k,lare the Miller indices.

a is the side of the unit cell.

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

nλ=2dsinθ …(2)

Where,

λ is the wavelength of incident ray.

d is the distance between two parallel planes.

θ is the Bragg’s angle.

n is the order of diffraction.

Substitute equation (1) in equation (2).

nλ=2(ah2+k2+l2)sinθsinθ=nλh2+k2+l22a

The above formula can be written as follows:

θ=sin1(nλh2+k2+l22a) …(3)

The given plane is (110). The side of the unit cell is 2.88A. The wavelength of X rays is 1.544A.

Substitute the value of (h,k,l), side and wavelength in equation (3).

θ=sin1(1×1.544A×12+12+022×2.88A)θ=sin10.3790878θ=22.3°

Thus, the angle by which the X rays would be diffracted by the (110) plane of atoms 22.3°.

Conclusion

The angle by which the X rays would be diffracted by the (110) plane of atoms 22.3°.

Expert Solution
Check Mark
Interpretation Introduction

(c)

Interpretation:

The angle would the X rays be diffracted by the (100) plane of atoms is to be determined.

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. Unit cell can be a cubic unit cell or hexagonal unit cell. The classification of a unit cell depends on the lattice site occupied by the atoms.

Answer to Problem 21.34E

The angle by which the X rays would be diffracted by the (210) plane of atoms 36.8°.

Explanation of Solution

The d spacing is calculated by formula as shown below.

d=ah2+k2+l2 …(1)

Where,

h,k,lare the Miller indices.

a is the side of the unit cell.

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

nλ=2dsinθ …(2)

Where,

λ is the wavelength of incident ray.

d is the distance between two parallel planes.

θ is the Bragg’s angle.

n is the order of diffraction.

Substitute equation (1) in equation (2).

nλ=2(ah2+k2+l2)sinθsinθ=nλh2+k2+l22a

The above formula can be written as follows:

θ=sin1(nλh2+k2+l22a) …(3)

The given plane is (210). The side of the unit cell is 2.88A. The wavelength of X rays is 1.544A.

Substitute the value of (h,k,l), side and wavelength in equation (3).

θ=sin1(1×1.544A×22+12+022×2.88A)θ=sin10.59939044θ=36.8°

Thus, the angle by which the X rays would be diffracted by the (210) plane of atoms 36.8°.

Conclusion

The angle by which the X rays would be diffracted by the (210) plane of atoms 36.8°.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
please
please help me please please
Using reaction free energy to predict equilibrium composition Consider the following equilibrium: N2 (g) + 3H2 (g) = 2NH3 (g) AG⁰ = -34. KJ Now suppose a reaction vessel is filled with 8.06 atm of nitrogen (N2) and 2.58 atm of ammonia (NH3) at 106. °C. Answer the following questions about this system: ? rise Under these conditions, will the pressure of N2 tend to rise or fall? ☐ x10 fall Is it possible to reverse this tendency by adding H₂? In other words, if you said the pressure of N2 will tend to rise, can that be changed to a tendency to fall by adding H₂? Similarly, if you said the pressure of N2 will tend to fall, can that be changed to a tendency to rise by adding H₂? If you said the tendency can be reversed in the second question, calculate the minimum pressure of H₂ needed to reverse it. Round your answer to 2 significant digits. yes no ☐ atm ☑ 5 00. 18 Ar

Chapter 21 Solutions

Student Solutions Manual for Ball's Physical Chemistry, 2nd

Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781337399074
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning
Text book image
Chemistry: Principles and Practice
Chemistry
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Cengage Learning
Text book image
Principles of Modern Chemistry
Chemistry
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:Cengage Learning
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781133949640
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning
Text book image
Chemistry for Engineering Students
Chemistry
ISBN:9781337398909
Author:Lawrence S. Brown, Tom Holme
Publisher:Cengage Learning
Text book image
Chemistry: The Molecular Science
Chemistry
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:Cengage Learning
Unit Cell Chemistry Simple Cubic, Body Centered Cubic, Face Centered Cubic Crystal Lattice Structu; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=HCWwRh5CXYU;License: Standard YouTube License, CC-BY