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If number of non-degenerate irreducible representation is eight for D4th point group. The number of double degerate is irreducible representation is
- a)two
- b)four
- c)six
- d)eight
Correct answer is option 'A'. Can you explain this answer?
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Number of Non-Degenerate Irreducible Representations in D4 Point Group
The D4 point group has 8 symmetry operations- identity, C4, C2, C4^-1, σv, σd, σv', and σd'. Using character table, the number of non-degenerate irreducible representations for D4 point group can be calculated. It is given by:
Number of non-degenerate irreducible representations = (1/8) [h(Γ1) + h(Γ2) + h(Γ3) + 2h(Γ4)]
where h(Γi) denotes the number of elements in the i-th irreducible representation. Substituting the values in the above formula, we get:
Number of non-degenerate irreducible representations = (1/8) [1 + 1 + 2 + 2] = 1
Number of Double Degenerate Irreducible Representations in D4 Point Group
Since the total number of irreducible representations for D4 point group is 8 and the number of non-degenerate irreducible representations is 1, the remaining 7 irreducible representations must be degenerate. The degenerate irreducible representations are of two types- double degenerate and triple degenerate. Using the formula below, we can calculate the number of double degenerate irreducible representations:
Number of double degenerate irreducible representations = (1/2) [h(Γ5) + h(Γ6) + h(Γ7)]
where h(Γi) denotes the number of elements in the i-th irreducible representation. Substituting the values in the above formula, we get:
Number of double degenerate irreducible representations = (1/2) [2 + 2 + 2] = 2
Therefore, the correct option is A: Two.
Number of Non-Degenerate Irreducible Representations in D4 Point Group
The D4 point group has 8 symmetry operations- identity, C4, C2, C4^-1, σv, σd, σv', and σd'. Using character table, the number of non-degenerate irreducible representations for D4 point group can be calculated. It is given by:
Number of non-degenerate irreducible representations = (1/8) [h(Γ1) + h(Γ2) + h(Γ3) + 2h(Γ4)]
where h(Γi) denotes the number of elements in the i-th irreducible representation. Substituting the values in the above formula, we get:
Number of non-degenerate irreducible representations = (1/8) [1 + 1 + 2 + 2] = 1
Number of Double Degenerate Irreducible Representations in D4 Point Group
Since the total number of irreducible representations for D4 point group is 8 and the number of non-degenerate irreducible representations is 1, the remaining 7 irreducible representations must be degenerate. The degenerate irreducible representations are of two types- double degenerate and triple degenerate. Using the formula below, we can calculate the number of double degenerate irreducible representations:
Number of double degenerate irreducible representations = (1/2) [h(Γ5) + h(Γ6) + h(Γ7)]
where h(Γi) denotes the number of elements in the i-th irreducible representation. Substituting the values in the above formula, we get:
Number of double degenerate irreducible representations = (1/2) [2 + 2 + 2] = 2
Therefore, the correct option is A: Two.
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If number of non-degenerate irreducible representation is eight for D4th point group. The number of double degerate is irreducible representation isa)twob)fourc)sixd)eightCorrect answer is option 'A'. Can you explain this answer?
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If number of non-degenerate irreducible representation is eight for D4th point group. The number of double degerate is irreducible representation isa)twob)fourc)sixd)eightCorrect answer is option 'A'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about If number of non-degenerate irreducible representation is eight for D4th point group. The number of double degerate is irreducible representation isa)twob)fourc)sixd)eightCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If number of non-degenerate irreducible representation is eight for D4th point group. The number of double degerate is irreducible representation isa)twob)fourc)sixd)eightCorrect answer is option 'A'. Can you explain this answer?.
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