Student Solutions Manual for Ball's Physical Chemistry, 2nd
2nd Edition
ISBN: 9798214169019
Author: David W. Ball
Publisher: Cengage Learning US
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Textbook Question
Chapter 13, Problem 13.46E
Show that any two of the irreducible representations of the following point groups are orthogonal to each other.
(a)
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(c) Using POC13 as an example, develop the
reducible representation of its point
group.
(a) Given the operator = -0 C₁¹ show that [‚Â] = 0
=0
(b) Decompose the representation below into the irreducible representations of C3v.
C3v
T
E
17/0
2C3
1
30₂
1
]
]
(c) With the use of diagrams, find the representation of the C₂ point group to which a day orbital
belongs.
]
Neopentane, C(CH3)4, has Tď symmetry, with character table provided below. Suppose the
characters of a reducible representation of this point group are x(E) = 17, x(C3) = 2, x(C₂) = 5,
x(S4) = -3, and x(od) = -5 (this is shown explicitly in the last row of the character table).
(a) Use the T₁ irreducible representation to determine the order of the point group using
the Little Orthogonality Theorem (Vallance Eq. 1.15.13, see Problem 3).
(b) Determine how many times each irreducible representation in Ta is contained in this
reducible representation.
Td
A₁
A₂
E
Τ1
T₂
r
E
1
1
2
3
3
17
8C3
1
1
-1
1 0 0 2
3C₂
1
1
2
-1
6S4
1
-1
1 101 1.5
7 0 1 713
7. 1.5
-1
-1
60d
-3
-1
-1
-5
Chapter 13 Solutions
Student Solutions Manual for Ball's Physical Chemistry, 2nd
Ch. 13 - In your own words, explain why an object that has...Ch. 13 - Identify the symmetry elements present in the...Ch. 13 - Identify the symmetry elements present in the...Ch. 13 - Prob. 13.4ECh. 13 - Prob. 13.5ECh. 13 - Prob. 13.6ECh. 13 - Prob. 13.7ECh. 13 - Prob. 13.8ECh. 13 - Any axis of symmetry Cn that rotates an object by...Ch. 13 - Prob. 13.10E
Ch. 13 - Prob. 13.11ECh. 13 - Prob. 13.12ECh. 13 - Prob. 13.13ECh. 13 - What are the number of classes and the order of...Ch. 13 - Prob. 13.15ECh. 13 - a Show that the C3v point group satisfies the...Ch. 13 - a In the Td point group, an S41 improper rotation...Ch. 13 - Determine which single symmetry operation of the...Ch. 13 - Prob. 13.19ECh. 13 - Prob. 13.20ECh. 13 - Prob. 13.21ECh. 13 - Figure 13.27 shows the structure of the molecule...Ch. 13 - Prob. 13.23ECh. 13 - Identify all the symmetry elements present in the...Ch. 13 - Point groups are called such because all of the...Ch. 13 - Determine the point groups of the following...Ch. 13 - Determine the point group of the following...Ch. 13 - Determine the point groups of the following...Ch. 13 - Determine the point groups of the following...Ch. 13 - Structural isomers can have very different point...Ch. 13 - Structural isomers can have very different point...Ch. 13 - Prob. 13.32ECh. 13 - Identify the point group of the wave functions of...Ch. 13 - Identify the point group of the wave functions of...Ch. 13 - Prob. 13.35ECh. 13 - Determine if the following species have permanent...Ch. 13 - Determine if the following species have permanent...Ch. 13 - Which of the following species will not have...Ch. 13 - Prob. 13.39ECh. 13 - Explain why a molecule with a center of inversion...Ch. 13 - a Unlike methane, bromochlorofluoromethane...Ch. 13 - Prob. 13.42ECh. 13 - Prob. 13.43ECh. 13 - Prob. 13.44ECh. 13 - Show that the irreducible representations of the...Ch. 13 - Show that any two of the irreducible...Ch. 13 - Show that any irreducible representation of these...Ch. 13 - Explain why this proposed irreducible...Ch. 13 - Prob. 13.49ECh. 13 - Prob. 13.50ECh. 13 - Why is it unnecessary to consider whether an...Ch. 13 - Prob. 13.52ECh. 13 - Prob. 13.53ECh. 13 - Prob. 13.54ECh. 13 - Prob. 13.55ECh. 13 - Prob. 13.56ECh. 13 - Prob. 13.57ECh. 13 - Prob. 13.58ECh. 13 - Reduce the following reducible representations...Ch. 13 - Determine the resulting representations for the...Ch. 13 - Prob. 13.61ECh. 13 - Without using the great orthogonality theorem,...Ch. 13 - Assume that you are evaluating the integral of...Ch. 13 - Prob. 13.64ECh. 13 - Assume that x- polarized light can be assigned an...Ch. 13 - Prob. 13.66ECh. 13 - Prob. 13.67ECh. 13 - Prob. 13.68ECh. 13 - Prob. 13.69ECh. 13 - Prob. 13.70ECh. 13 - Construct the symmetry-adapted linear combination...Ch. 13 - Prob. 13.72ECh. 13 - Prob. 13.73ECh. 13 - Prob. 13.74ECh. 13 - Prob. 13.75ECh. 13 - Prob. 13.76ECh. 13 - Prob. 13.77ECh. 13 - Suppose you use p0,p1 and p+1 along with s...Ch. 13 - Show that the individual sp orbitals, as written...Ch. 13 - Prob. 13.80ECh. 13 - What is the rough hybridization of the carbon...Ch. 13 - Determine the symmetry species of the D3h point...Ch. 13 - Determine the D3h symmetry species of the sp3d...Ch. 13 - Prob. 13.84ECh. 13 - In propene CH3CH=CH2, the first carbon has sp3...Ch. 13 - Prob. 13.87ECh. 13 - Prob. 13.88ECh. 13 - Prob. 13.89E
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