Concept explainers
Interpretation:
The angle of diffraction has to be calculated.
Concept introduction:
Bragg equation:
Bragg diffraction occurs when radiation, with a wavelength comparable to atomic spacing is scattered in a regular fashion by the atoms of a crystalline system and undergoes constructive interference. For a crystalline solid the waves are scattered from lattice planes separated by the interplanar distance
Figure 1
The Bragg equation is,
Where,
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Chemistry: Principles and Practice
- 8.98 If you know the density of material and the length of the edge of its cubic Iattice, how would you determine if it is face-centered cubic, body-centered cubic, or simple cubic Would you have to look up any information?arrow_forwardPalladium has a cubic crystal structure in which the edge of the unit cell is 389 pm long. If the density of palladium is 12.02 g/cm3, how many palladium atoms are in a unit cell? In which of the cubic unit cells does palladium crystallize?arrow_forward8.16 Iridium forms a face-centered cubic lattice, and an iridium atom is 271.4 pm in diameter. Calculate the density of iridium.arrow_forward
- What is the value of 0 for the first diffraction line (n = 1) in bcc iron (atomic radius 126 pm) when the X-ray wavelength is 58.0 pm? Hint: Consider the closest set of lattice planes.arrow_forwardThe surface energy of a single crystal depends on crystallographic orientation. Does this surface energy increase or decrease with an increase in planar density? Why?arrow_forwardIf the wavelength l of the X-rays is too large relative to the spacing of planes in the crystal, no Bragg diffraction will be seen because sin u would be larger than 1 in the Bragg equation, even for n = 1. Calculate the longestwavelength of Xrays that can give Bragg diffraction from a set of planes separated by 4.20 Å.arrow_forward
- When an X-ray beam of l = 154 pm is incident on the surface of an iron crystal, it produces a maximum diffraction at an angle of u = 32.6°. Assuming n = 1, calculate the separation between layers of iron atoms in the crystal.arrow_forwardThe second-order Bragg diffraction of X-rays with /l= 1.237 Å from a set of parallel planes in aluminum occurs at an angle 2Q = 35.58°. Calculate the distance between the scattering planes in the crystal.arrow_forwardWhat are the values of 2 theta for the first 3 diffraction lines of FCC gold (atomic radius 144 pm) when the x-ray wavelength is 154 pm?arrow_forward
- A first-order (n = 1) reflection from the plane of a cubic crystal was observed at a glancing angle of 11.2° when Cu Ka X-rays (λ = 154 pm) were used. What is the interatomic distance between the atoms in the unit cell in pm?arrow_forwardWhen an electron beam penetrates a sample in the SEM microscope chamber, the properties of the electron beam (i.e., its energy, E, or equivalently, wavelengthe) are related to the spacing of the atomic planes, d, through the Bragg's diffraction relation: nλ = 2d sin 0 Where n is the integer order of diffraction. When Bragg's condition for a certain set of planes is met, a diffraction pattern can be produced and collected by a detector in order to analyze the crystal orientations and texture of the grains. Consider an incident beam energy of (1.47x10^1) keV, where the electron wavelength is given by the de Broglie equation: de = h 2m (Eo " where m is the mass of an electron and E is expressed in joules. If the electron beam is directed at a silicon crystal that has a diamond-cubic crystal lattice with a lattice parameter of (4.8800x10^-10) meters, what is the value of the incident angle (0) produced to satisfy the first order diffraction of the (220) plane? Express you answer in…arrow_forwardElemental silver reflects X-rays of wavelength 154.18 pm at angles of 19.076°, 22.171°, and 32.256°. However, there are no other reflections at angles of less than 33°. Assuming a cubic unit cell, determine its type and dimension. Calculate the mass density of silver. Hint: Calculate the expected reflections from different types of cubic unit cell and compare those with the data given.arrow_forward
- Chemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage LearningGeneral Chemistry - Standalone book (MindTap Cour...ChemistryISBN:9781305580343Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; DarrellPublisher:Cengage LearningPrinciples of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage Learning
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Chemistry for Engineering StudentsChemistryISBN:9781337398909Author:Lawrence S. Brown, Tom HolmePublisher:Cengage LearningChemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage Learning