TRB PG Assistant - Symmetry elements, operations, point groups and character tables for common groups Online Test (MCQ Quiz)

1. What is the fundamental property of a symmetry operation that leaves a molecule unchanged after its application?

A) Change in molecular geometry B) Inversion of atomic coordinates C) No net change in molecular configuration D) Rotation of the molecule by 180 degrees

2. Which symmetry element consists of an axis about which rotation by 360/n degrees leaves the molecule indistinguishable?

A) Plane of symmetry (σ) B) Center of inversion (i) C) Identity element (E) D) Axis of rotation (Cn)

3. What does the symbol 'E' represent in the context of symmetry operations?

A) An axis of rotation B) A plane of symmetry C) The identity operation D) A center of inversion

4. A plane of symmetry (σ) is a plane that divides a molecule into two mirror images that are:

A) Identical but not superimposable B) Superimposable mirror images C) Completely different in structure D) Rotated by 90 degrees

5. Which symmetry operation involves reflecting the molecule through a plane of symmetry?

A) Rotation (Cn) B) Identity (E) C) Reflection (σ) D) Inversion (i)

6. The symbol 'i' denotes which symmetry element?

A) Axis of rotation B) Center of inversion C) Plane of symmetry D) Improper rotation axis

7. An improper rotation axis (Sn) involves rotation by 360/n degrees followed by:

A) Identity operation B) Reflection through a plane perpendicular to the axis C) Inversion through the center D) Rotation by 180 degrees

8. What is the point group of a molecule that possesses only the identity element (E)?

A) C1 B) Cs C) Ci D) T

9. A molecule with only a plane of symmetry (σ) and the identity element (E) belongs to which point group?

A) C1 B) Cs C) Ci D) C2

10. If a molecule has only a center of inversion (i) and the identity element (E), its point group is:

A) Cs B) Ci C) C2 D) Cnv

11. Which point group describes linear molecules like CO2 (ignoring vibrational modes)?

A) D∞h B) C∞v C) C2v D) Oh

12. What is the point group for a diatomic molecule like O2?

A) C∞v B) D∞h C) C2v D) D2h

13. A molecule with a single C2 axis and two vertical planes of symmetry (σv) perpendicular to each other belongs to which point group?

A) C2v B) D2h C) C2h D) D2

14. 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?

A) Benzene B) Water C) Methane D) Ammonia

15. What is the point group of ammonia (NH3)?

A) C3v B) D3h C) C3h D) C3

16. Which point group characterizes molecules with a Cn axis, n C2 axes perpendicular to the Cn axis, and a horizontal plane of symmetry (σh)?

A) Cnh B) Dnh C) Dnd D) S2n

17. Benzene (C6H6) belongs to which point group?

A) D6h B) C6v C) D3h D) D6

18. What is the point group of methane (CH4), considering its tetrahedral symmetry?

A) Td B) Oh C) Th D) I

19. The point group Oh describes molecules with octahedral symmetry. Which molecule exhibits this symmetry?

A) SF6 B) CCl4 C) BF3 D) XeF4

20. A character table in group theory summarizes the properties of:

A) Molecular orbitals B) Symmetry operations and irreducible representations C) Bond lengths and angles D) Thermodynamic parameters

21. In a character table, what does the symbol 'χ' represent?

A) A symmetry operation B) A class of symmetry operations C) The character of an irreducible representation D) An irreducible representation

22. What is the significance of the first column in a character table?

A) Symmetry operations B) Classes of symmetry operations C) Irreducible representations D) Characters of the identity operation

23. The sum of the squares of the characters in each row (representing an irreducible representation) of a character table is equal to:

A) The number of symmetry operations B) The order of the group C) The number of classes D) The number of atoms in the molecule

24. The number of irreducible representations in a character table is equal to the number of:

A) Symmetry operations B) Classes of symmetry operations C) Atoms in the molecule D) Molecular orbitals

25. What does the dimension of an irreducible representation represent in a character table?

A) The number of symmetry operations in its class B) The number of electrons in the molecule C) The number of basis functions transforming as that representation D) The total number of orbitals

26. Which irreducible representation typically has a character of 1 for all symmetry operations?

A) T B) A or B C) E D) F

27. In character tables for groups with a horizontal symmetry plane (σh), what does the subscript 'g' or 'u' indicate?

A) Gerade (even) or Ungerade (odd) with respect to inversion B) Ground state or Excited state C) General or Unique D) Group theory or Representation

28. The irreducible representation 'E' in a character table typically has a dimension of:

A) 1 B) 2 C) 3 D) 4

29. The irreducible representation 'T' or 'F' in a character table typically has a dimension of:

A) 1 B) 2 C) 3 D) 4

30. For the C2v point group, which symmetry operation is NOT in the same class as C2?

A) E B) σv(xz) C) σv'(yz) D) C2

31. 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?

A) E B) σ C) i D) C2(x), C2(y), C2(z)

32. Which symmetry operation is always present in every point group?

A) C2 B) σh C) E D) i

33. What is the order of the C3v point group?

A) 3 B) 4 C) 6 D) 9

34. How many classes of symmetry operations are there in the D3h point group?

A) 3 B) 4 C) 5 D) 6

35. The symmetry of a molecule determines its:

A) Chemical reactivity only B) Spectroscopic properties only C) Both spectroscopic properties and chemical reactivity D) Thermodynamic stability only

36. In molecular spectroscopy, symmetry helps in determining:

A) The number of electronic transitions B) Selection rules for transitions C) The rate of radioactive decay D) The molecular weight

37. Which symmetry element is NOT present in the C2h point group?

A) E B) C2 C) σh D) σv

38. The point group of formaldehyde (CH2O) is:

A) C2v B) D2h C) C2h D) C2

39. Which of the following molecules belongs to the Td point group?

A) SF6 B) XeF4 C) CCl4 D) H2O

40. What is the correct point group for a planar equilateral triangle with identical atoms at each vertex, like BF3?

A) C3v B) D3h C) C3h D) D3

41. The character table for which point group is used to describe the vibrational modes of a linear molecule like CO2?

A) C∞v B) D∞h C) C2v D) D2h

42. In group theory, a set of symmetry operations that obey group postulates is called a:

A) Symmetry element B) Point group C) Irreducible representation D) Character

43. Which symmetry operation is not present in the D3 point group?

A) E B) C3 C) C2 D) σh

44. The irreducible representation that corresponds to the translation of the molecule along the z-axis is often denoted as:

A) A1 B) B1 C) T1u D) A2

45. What is the point group of a molecule possessing only a C3 axis and three C2 axes perpendicular to it?

A) D3 B) D3h C) D3d D) C3

46. 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?

A) Cnh B) Dnh C) S2n D) Cn

47. The character table for the Td point group contains how many irreducible representations?

A) 4 B) 5 C) 6 D) 7

48. Which of the following is a symmetry operation of the octahedral (Oh) point group?

A) C3 B) C5 C) S6 D) C4

49. The character table is essential for determining the degeneracy of molecular vibrations and electronic states based on their:

A) Molecular formula B) Point group symmetry C) Bond order D) Mass number

50. What is the symmetry element for a C2 axis where rotation by 180 degrees results in an indistinguishable molecule?

A) Plane of symmetry B) Identity element C) Axis of rotation (C2) D) Center of inversion

Symmetry elements, operations, point groups and character tables for common groups - Online Test

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