(a)
Interpretation:
The number of Raman-active vibrations for the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
Answer to Problem 14.94E
The number of Raman-active vibrations for the
Explanation of Solution
The symmetry of
The character table for point group
operations | |||||
This reducible representation reduced using great orthogonality theorem as shown below.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The order of the group is
The great orthogonality theorem orthogonality of the irreducible representation of
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
The character of
Therefore,
Therefore, there are four Raman-active vibrations and two IR-active vibrations would be observed by
Therefore, the number of Raman-active vibrations for the
The number of Raman-active vibrations for the
(b)
Interpretation:
The number of Raman-active vibrations for the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
Answer to Problem 14.94E
The number of Raman-active vibrations for the
Explanation of Solution
The symmetry of
The character table for point group
operations | |||
This reducible representation reduced using great orthogonality theorem as shown below.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The order of the group is
The great orthogonality theorem orthogonality of the irreducible representation of
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
The character of
Therefore,
The
Therefore, there are six Raman-active vibrations and six IR-active vibrations would be observed by
Therefore, the number of Raman-active vibrations for the
The number of Raman-active vibrations for the
(c)
Interpretation:
The number of Raman-active vibrations for the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
Answer to Problem 14.94E
The number of Raman-active vibrations for the
Explanation of Solution
The symmetry of
The character table for point group
operations | ||||
This reducible representation reduced using great orthogonality theorem as shown below.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The order of the group is
The great orthogonality theorem orthogonality of the irreducible representation of
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Therefore,
The
The
The
Therefore, there are nine Raman-active vibrations and eight IR-active vibrations would be observed by
Therefore, the number of Raman-active vibrations for the
The number of Raman-active vibrations for the
(d)
Interpretation:
The number of Raman-active vibrations for the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
Answer to Problem 14.94E
The number of Raman-active vibrations for the
Explanation of Solution
The symmetry of
The character table for point group
operations | |||
This reducible representation reduced using great orthogonality theorem as shown below.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The order of the group is
The great orthogonality theorem orthogonality of the irreducible representation of
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
The character of
Therefore,
The
Therefore, there are six Raman-active vibrations and six IR-active vibrations would be observed by
Therefore, the number of Raman-active vibrations for the
The number of Raman-active vibrations for the
(e)
Interpretation:
The number of Raman-active vibrations for the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
Answer to Problem 14.94E
The number of Raman-active vibrations for the
Explanation of Solution
The symmetry of
The character table for point group
operations | |||||
This reducible representation reduced using great orthogonality theorem as shown below.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The order of the group is
The great orthogonality theorem orthogonality of the irreducible representation of
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
The character of
Therefore,
Therefore, there are four Raman-active vibrations and two IR-active vibrations would be observed by
Therefore, the number of Raman-active vibrations for the
The number of Raman-active vibrations for the
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Chapter 14 Solutions
Physical Chemistry
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- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage Learning