Physical Chemistry

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



Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437
Chapter 21, Problem 21.24E
Textbook Problem

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


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)


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).


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

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 21 Solutions

Physical Chemistry
Show all chapter solutions
Ch. 21 - Use geometry to determine the largest atom that...Ch. 21 - What is the maximum percentage volume that can be...Ch. 21 - Prove the relationship in equation 21.3.Ch. 21 - Zinc selenide, ZnSe, is a bright-orange compound...Ch. 21 - Pyrite is a gold-colored mineral that is also...Ch. 21 - Talc is a complex silicate mineral having the...Ch. 21 - One form of quartz, SiO2, has a hexagonal unit...Ch. 21 - Speculate on why the hexagonal unit cell is called...Ch. 21 - Table 21.7, listing some unit-cell parameters, has...Ch. 21 - Using the data in Table 21.7, determine the...Ch. 21 - At least 43 of the elements that are composed of...Ch. 21 - Explain why zeroth-order X-ray diffraction does...Ch. 21 - Use geometry to derive a form of Braggs law in...Ch. 21 - Although first-order diffractions might occur at...Ch. 21 - Determine the angle of the first- and second-order...Ch. 21 - Certain X rays generated by bombarding metallic...Ch. 21 - 56Fe crystallizes in a body-centered unit cell...Ch. 21 - For a simple cubic lattice, what Miller indices...Ch. 21 - For a simple cubic lattice, what is the ratio of...Ch. 21 - For face-centered cubic lattice, what are the...Ch. 21 - Because crystals exist in three dimensions, 3-D...Ch. 21 - Consider Figure 21.21. If the lower rightmost...Ch. 21 - Any one plane can be described by more than one...Ch. 21 - The aluminum-nickel alloy AlNi has a simple cubic...Ch. 21 - A powdered sample diffracts X rays (=1.5418A) at...Ch. 21 - The first two signals from a powdered sample has X...Ch. 21 - A crystallographer calculates values of (h2+k2+l2)...Ch. 21 - Predict the angles of diffraction of X rays having...Ch. 21 - Use geometric arguments to illustrate why the...Ch. 21 - Explain why the X-ray diffraction pattern of CuZn,...Ch. 21 - A given X-ray diffraction pattern is composed of...Ch. 21 - Predict the unit cells for the following...Ch. 21 - Predict the unit cells for the following...Ch. 21 - Sulfur, S, has some interesting solid-solid phase...Ch. 21 - Explain why the element carbon does not have a...Ch. 21 - What is the coordination number in the cesium...Ch. 21 - Determine the coordination numbers of the ions in...Ch. 21 - Which solid phase that is, which allotrope of...Ch. 21 - Write the specific chemical reactions whose...Ch. 21 - Explain why lattice energy is considered a form of...Ch. 21 - Write Born-Haber cycles showing the relationship...Ch. 21 - Compare the two-particle coulombic energy of...Ch. 21 - Using the data in Table 21.6, calculate the...Ch. 21 - Using the data in Table 21.6, calculate the...Ch. 21 - The lattice energy for potassium iodide, KI, is...Ch. 21 - The concept of charge density involves the total...Ch. 21 - Lattice energies can also be defined for atomic...Ch. 21 - Studies of crystals of He, Ne, and Ar and so on...Ch. 21 - Solid palladium metal is known to actually absorb...Ch. 21 - Gallium arsenide (GaAs) can also serve as a basis...Ch. 21 - Suggest dopants for GaAs that would yield a a...Ch. 21 - Explain how holes conduct electricity.Ch. 21 - Calculate the volume of the unit cells for the...Ch. 21 - Set up a program or formula to calculate the...

Additional Science Textbook Solutions

Find more solutions based on key concepts
Show solutions add
Determine the mass percentage of carbon in CO and CO2.

Chemistry for Today: General, Organic, and Biochemistry

The National Center for Complementary and Alternative Medicine fNCCAMl promotes laetrile therapy. T F

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

What is physically exchanged during crossing over?

Human Heredity: Principles and Issues (MindTap Course List)

________ is lifes primary source of energy. a. Food b. Water c. Sunlight d. ATP

Biology: The Unity and Diversity of Life (MindTap Course List)

A rocket for use in deep space is to be capable of boosting a total load (payload plus rocket frame and engine)...

Physics for Scientists and Engineers, Technology Update (No access codes included)

How can sound be used to measure the temperature of an ocean?

Oceanography: An Invitation To Marine Science, Loose-leaf Versin