Symmetry elements, operations, point groups and character tables for common groups - Question Bank
1. What is the symmetry element for a C2 axis where rotation by 180 degrees results in an indistinguishable molecule?
2. The character table is essential for determining the degeneracy of molecular vibrations and electronic states based on their:
3. Which of the following is a symmetry operation of the octahedral (Oh) point group?
4. The character table for the Td point group contains how many irreducible representations?
5. If a molecule has a center of inversion and a horizontal plane of symmetry, it belongs to a Cnh or Dnh point group. Which of these is more likely for a molecule with multiple C2 axes perpendicular to the principal axis?
6. What is the point group of a molecule possessing only a C3 axis and three C2 axes perpendicular to it?
7. The irreducible representation that corresponds to the translation of the molecule along the z-axis is often denoted as:
8. Which symmetry operation is not present in the D3 point group?
9. In group theory, a set of symmetry operations that obey group postulates is called a:
10. The character table for which point group is used to describe the vibrational modes of a linear molecule like CO2?
11. What is the correct point group for a planar equilateral triangle with identical atoms at each vertex, like BF3?
12. Which of the following molecules belongs to the Td point group?
13. The point group of formaldehyde (CH2O) is:
14. Which symmetry element is NOT present in the C2h point group?
15. In molecular spectroscopy, symmetry helps in determining:
16. The symmetry of a molecule determines its:
17. How many classes of symmetry operations are there in the D3h point group?
18. What is the order of the C3v point group?
19. Which symmetry operation is always present in every point group?
20. In the D2h point group, the operation 'i' (inversion) is in a class by itself. What other operations are typically in the same class as C2 axes?
21. For the C2v point group, which symmetry operation is NOT in the same class as C2?
22. The irreducible representation 'T' or 'F' in a character table typically has a dimension of:
23. The irreducible representation 'E' in a character table typically has a dimension of:
24. In character tables for groups with a horizontal symmetry plane (σh), what does the subscript 'g' or 'u' indicate?
25. Which irreducible representation typically has a character of 1 for all symmetry operations?
26. What does the dimension of an irreducible representation represent in a character table?
27. The number of irreducible representations in a character table is equal to the number of:
28. The sum of the squares of the characters in each row (representing an irreducible representation) of a character table is equal to:
29. What is the significance of the first column in a character table?
30. In a character table, what does the symbol 'χ' represent?
31. A character table in group theory summarizes the properties of:
32. The point group Oh describes molecules with octahedral symmetry. Which molecule exhibits this symmetry?
33. What is the point group of methane (CH4), considering its tetrahedral symmetry?
34. Benzene (C6H6) belongs to which point group?
35. Which point group characterizes molecules with a Cn axis, n C2 axes perpendicular to the Cn axis, and a horizontal plane of symmetry (σh)?
36. What is the point group of ammonia (NH3)?
37. The point group Cnv describes molecules with a Cn axis and n vertical planes of symmetry passing through the axis. What is an example of a C2v molecule?
38. A molecule with a single C2 axis and two vertical planes of symmetry (σv) perpendicular to each other belongs to which point group?
39. What is the point group for a diatomic molecule like O2?
40. Which point group describes linear molecules like CO2 (ignoring vibrational modes)?
41. If a molecule has only a center of inversion (i) and the identity element (E), its point group is:
42. A molecule with only a plane of symmetry (σ) and the identity element (E) belongs to which point group?
43. What is the point group of a molecule that possesses only the identity element (E)?
44. An improper rotation axis (Sn) involves rotation by 360/n degrees followed by:
45. The symbol 'i' denotes which symmetry element?
46. Which symmetry operation involves reflecting the molecule through a plane of symmetry?
47. A plane of symmetry (σ) is a plane that divides a molecule into two mirror images that are:
48. What does the symbol 'E' represent in the context of symmetry operations?
49. Which symmetry element consists of an axis about which rotation by 360/n degrees leaves the molecule indistinguishable?
50. What is the fundamental property of a symmetry operation that leaves a molecule unchanged after its application?