Q122 · CSIR-NET Chemistry, June 2011
Paper: CSIR-NET June 2011 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Character Tables · Marks: 2 · Difficulty: Easy
The $\mathrm{E} \times \mathrm{E}$ direct product in $\mathrm{D}_{3}$ point group contains the irreducible representations | $\mathrm{D}_{3}$ | E | $2 \mathrm{C}_{3}$ | $3 \mathrm{C}_{2}$ |
|---|
| $\mathrm{A}_{1}$ | 1 | 1 | -1 |
| $\mathrm{A}_{2}$ | 1 | 1 | -1 |
| $\mathrm{E}_{2}$ | 2 | -1 | 0 |
(a)$\mathrm{A}_{1}+\mathrm{A}_{2}+\mathrm{E}$
(b)$2 \mathrm{A}_{1}+\mathrm{E}$
(c)$2 \mathrm{A}_{2}+\mathrm{E}$
(d)$2 \mathrm{A}_{1}+2 \mathrm{A}_{2}$
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
In D₃, E × E = A₁ + A₂ + E (characters 4, 1, 0).
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