## Character Table Analysis for Point Group Symmetry### Missing Information in Character TableThe table below is a character table for a point group associated with a molecule (BH₃). Some information, including symmetry elements and functions, is missing and needs to be determined.| | E | 2 C₃ | 3 C₂ | ? | 2 S₃ | 3 σᵥ | Basis Functions ||------|---|------|------|---|-----|------|-----------------|| X₁ | 1 | 1 | 1 | 1 | 1 | 1 | x² + y², z² || A₂' | 1 | 1 | -1 | 1 | 1 | -1 | Rz || E’ | 2 | -1 | 0 | 2 | -1 | 0 | (x, y) || A₁’’ | 1 | X₂ | 1 | -1 | -1 | -1 | || A₂’’ | 1 | 1 | -1 | -1 | -1 | 1 | X₃ || E’’ | 2 | -1 | 0 | -2 | 1 | 0 | (Rx, Ry) |- **Symmetry Operations:** - **C₃**: 120-degree rotation about the principal axis. - **C₂**: 180-degree rotation about a secondary axis. - **σᵥ**: Vertical mirror plane. - **S₃**: Improper rotation.### Questions**a. Missing Symmetry Element:** Identify the missing symmetry element represented by "?".**b. Missing Information in Table:**Determine the unknown values for X₁, X₂, and X₃.- **i. X₁ =**- **ii. X₂ =**- **iii. X₃ =****c. Orbital Symmetry Along C₃ Axis:**For this point group, identify the symmetry of the following orbitals for an atom located along the main C₃ axis:- **i. A pₓ orbital: ___________**- **ii. A d

The nature of the molecule that represents one part of it is the mirror image of the other part is…

The following character table (accompanied by a molecule of the corresponding point group) has some missing information. 2 C3 3 C2 2 S3 3 ov X1 1 1 1 1 1 1 x2+ y?, z2 1 1 -1 1 1 -1 Rz E' 2 -1 2 -1 (x, y) (x2- y?, xy) A;" 1 X2 1 -1 -1 -1 Az" 1 1 -1 -1 -1 1 X3 BH; E" -1 -2 1 (Rx, Ry) (2х, yz) а. Based on symmetry labels and Mulliken symbols, what is the missing symmetry element? b. Provide the missing information in the table: i. X1 = ii. X2 = iii. X3 = С. For this point group, what is the symmetry of the following orbitals for an atom located along the main C3 axis? i. A px orbital: ii. A d? orbital: iii. A dxy orbital:

The following character table (accompanied by a molecule of the corresponding point group) has some missing information. 2 C3 3 C2 2 S3 3 ov X1 1 1 1 1 1 1 x2+ y?, z2 1 1 -1 1 1 -1 Rz E' 2 -1 2 -1 (x, y) (x2- y?, xy) A;" 1 X2 1 -1 -1 -1 Az" 1 1 -1 -1 -1 1 X3 BH; E" -1 -2 1 (Rx, Ry) (2х, yz) а. Based on symmetry labels and Mulliken symbols, what is the missing symmetry element? b. Provide the missing information in the table: i. X1 = ii. X2 = iii. X3 = С. For this point group, what is the symmetry of the following orbitals for an atom located along the main C3 axis? i. A px orbital: ii. A d? orbital: iii. A dxy orbital:

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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