ABC26PH0468 · Group Theory
Subject: Physical Chemistry · Chapter: Group Theory · Topic: Reducible Representations · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Medium
The character table for a pyramidal $\mathrm{AB}_{3}$ molecule of $\mathrm{C}_{3 \mathrm{v}}$ point group is given below: | $\mathrm{C}_{3 \mathrm{v}}$ | E | $2 \mathrm{C}_{3}$ | $3 \sigma_{\mathrm{v}}$ |
|---|
| $\mathrm{A}_{1}$ | 1 | 1 | 1 | z | $\mathrm{x}^{2}+\mathrm{y}^{2}, \mathrm{z}^{2}$ |
| $\mathrm{A}_{2}$ | 1 | 1 | -1 | $\mathrm{R}_{\mathrm{z}}$ |
| E | 2 | -1 | 0 | $(\mathrm{x}, \mathrm{y})\left(\mathrm{R}_{\mathrm{x}}, \mathrm{R}_{\mathrm{y}}\right)$ | $\left(\mathrm{x}^{2}-\mathrm{y}^{2}, \mathrm{xy}\right)(\mathrm{xz}, \mathrm{yz})$ |
| $\mathrm{C}_{3 \mathrm{v}}$ | E | $2 \mathrm{C}_{3}$ | $3 \sigma_{\mathrm{v}}$ |
|---|
| Г | 12 | 0 | 2 |
(a)$\mathrm{A}_{1}+\mathrm{A}_{2}+2 \mathrm{E}$
(b)$2 \mathrm{A}_{1}+2 \mathrm{E}$
(c)$3 \mathrm{A}_{1}+\mathrm{A}_{2}+\mathrm{E}$
(d)3E
Answer
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Explanation
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