Worksheet: Point Groups

In this worksheet, we will practice finding the point group of a molecule by listing its inversion, reflection, rotation, and rotoinversion symmetries.

Q1:

By identifying all symmetry elements in ammonia (NH)3, assign the point group of the molecule.

  • A D h
  • B D h
  • C C v
  • D T d

Q2:

What is the point group of water?

  • A 𝐶 v
  • B 𝐷
  • C 𝐶 2 v
  • D 𝑇 d
  • E 𝐶

Q3:

A molecule has the following symmetries only: 𝐸, 𝐶, and 2𝜎v. What is the point group of the molecule?

  • A 𝐶 v
  • B 𝐶 v
  • C 𝐷
  • D 𝐶
  • E 𝑇 d

Q4:

A molecule is linear, without a center of inversion. What is its point group?

  • A 𝐷 h
  • B 𝐶 v
  • C 𝐶 i
  • D 𝐶
  • E 𝑂 h

Q5:

What is the point group of NH3?

  • A 𝑇 d
  • B 𝐶
  • C 𝐶 v
  • D 𝐷
  • E 𝐶 v

Q6:

A molecule has the following symmetries only: 𝐸, 𝐶, 𝐶, and 3𝜎v. What is the point group of this molecule?

  • A 𝐶 v
  • B 𝑇 d
  • C 𝐶 v
  • D 𝐷
  • E 𝐶

Q7:

What is the point group of HCl?

  • A 𝐶 i
  • B 𝐶 v
  • C 𝑂 h
  • D 𝐷 h
  • E 𝐶

Q8:

Which of the following has C4v symmetry?

  • A P C l 6
  • B H O 2
  • C B r F 5
  • D W ( C O ) 6
  • E B H 3

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