Inorganic Chemistry
5th Edition
ISBN: 9780321811059
Author: Gary L. Miessler, Paul J. Fischer, Donald A. Tarr
Publisher: Prentice Hall
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Chapter 4.1, Problem 4.1E
Interpretation Introduction
Interpretation: Using a point in a three dimensional Cartesian coordinate system, this needs to be shown that
Concept Introduction: The overall symmetry of a molecule is described by set of symmetry operations. This set of symmetry operations is known as point groups of the molecule.
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Consider the three spherical harmonics (a) Y0,0, (b) Y2,–1, and (c) Y3,+3. (a) For each spherical harmonic, substitute the explicit form of the function taken from Table 7F.1 into the left-hand side of eqn 7F.8 (the Schrödinger equation for a particle on a sphere) and confirm that the function is a solution of the equation; give the corresponding eigenvalue (the energy) and show that it agrees with eqn 7F.10. (b) Likewise, show that each spherical harmonic is an eigenfunction of lˆz = (ℏ/i)(d/dϕ) and give the eigenvalue in each case.
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Chapter 4 Solutions
Inorganic Chemistry
Ch. 4.1 - Prob. 4.1ECh. 4.1 - Find all the symmetry elements in the following...Ch. 4.2 - Use the procedure described previously to verify...Ch. 4.3 - Prob. 4.4ECh. 4.3 - Verify the transformation matrices for the E and...Ch. 4.3 - Prepare a representation flowchart according to...Ch. 4.4 - Which point groups are possible for chiral...Ch. 4.4 - Write the corresponding 99 transformation matrices...Ch. 4.4 - Using the x, y, and z coordinates for each atom in...Ch. 4.4 - Reduce the following representations to their...
Ch. 4.4 - Prob. 4.11ECh. 4.4 - Analysis of the x, y, and z coordinates of each...Ch. 4.4 - Determine the number of IR-active CO stretching...Ch. 4.4 - Prob. 4.14ECh. 4 - Determine the point groups for a. Ethane...Ch. 4 - Determine the point groups for a. Ethylene b....Ch. 4 - Determine the point groups for a. Acetylene b....Ch. 4 - Determine the point groups for a. Naphthalene b....Ch. 4 - Determine the point groups for a. 1,1’ ...Ch. 4 - Determine the point groups for a. Cyclohexane...Ch. 4 - Determine the point groups for a. A sheet of...Ch. 4 - Determine the point groups for a. A flat oval...Ch. 4 - Determine the point groups for a. A triangular...Ch. 4 - Determine the point groups for the examples of...Ch. 4 - Determine the point groups of the molecules in the...Ch. 4 - Determine the point groups of the molecules and...Ch. 4 - Determine the point groups of the following atomic...Ch. 4 - a. Show that a cube has the same symmetry elements...Ch. 4 - Suppose an octahedron can have either yellow or...Ch. 4 - What point groups are represented by the symbols...Ch. 4 - Prob. 4.17PCh. 4 - Determine the point groups for the following flags...Ch. 4 - Prepare a representation flowchart according to...Ch. 4 - For trans-1,2-dichloroethylene, which has C2h...Ch. 4 - Ethylene has D2h symmetry. a. List all the...Ch. 4 - Using the D2d character table, a. Determine the...Ch. 4 - Reduce the following representations to...Ch. 4 - For D4h symmetry use sketches to show that dxy...Ch. 4 - Prob. 4.25PCh. 4 - XeOF4 has one of the more interesting structures...Ch. 4 - Repeat the procedure from the previous problem,...Ch. 4 - For the following molecules, determine the number...Ch. 4 - Prob. 4.29PCh. 4 - The structure of 1,1,2,2-tetraiododisilane is...Ch. 4 - Both cis and trans isomers of IO2F4 have been...Ch. 4 - White elemental phosphorus consists of tetrahedral...Ch. 4 - Complexes of the general formula Fe(CO)5x( PR3)x...Ch. 4 - Prob. 4.35PCh. 4 - Prob. 4.36PCh. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Determine the point groups of the following...Ch. 4 - Prob. 4.40PCh. 4 - Determine the point groups of the following: a....Ch. 4 - Use the Internet to search for molecules with the...
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