Interpretation:
Whether the shape of xenon tetrafluoride,
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is that 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,
Answer to Problem 14.96E
The shape of xenon tetrafluoride,
Explanation of Solution
It is assumed that the shape of xenon tetrafluoride is tetrahedral.
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 are given by tetrahedral. This is not matched with the given information. Therefore, the shape of xenon tetrafluoride,
It is assumed that the shape of xenon tetrafluoride is square planar.
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
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
The character of
Therefore,
Therefore, there are three Raman-active vibrations and three IR-active vibrations are given by square planar. This is matched with the given information. Therefore, the shape of xenon tetrafluoride,
The shape of xenon tetrafluoride,
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Chapter 14 Solutions
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