2.4: Concept Review Questions Chapter 2

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Concept Review Questions

Section 1

1. What is the definition of symmetry, a symmetry operation, and a symmetry element?

2. There are five basic types of symmetry operations. Name them.

3. Of these five types of operations, two are not independent (i.e. they can be expressed by two of the three others). Name the two operations and explain why they are not independent.

4. What is the definition of the identity operation?

5. What is the definition of a proper rotational axis, and a proper rotation operation?

6. What is the definition of a mirror plane and a reflection operation?

7. What is the definition of an improper rotational axis and a rotation-reflection operation?

8. What is the definition of an inversion center and an inversion operation?

9. What is a principal axis?

10. What is the definition of a horizontal, vertical, and dihedral mirror plane, respectively?

11. What are the rules for giving axes and mirror planes primes?

12. How often do you have to carry out a proper rotation (order n), a reflection, an inversion, and a rotation-reflection (order n), respectively until you have reached the identity?

Section 2

1. What is a Platonic Solid?

2. Name the possible platonic solids.

3. Draw an icosahedron according to the rules that you have learned in class.

4. Which are the three low symmetry point groups? Which symmetry elements do they contain?

5. Name all high symmetry point groups.

6. What is a rotational subgroup?

7. What symmetry properties does a rotational point group have?

8. What symmetry properties does a dihedral point group have?

9. What different types of rotational point groups do you know?

10. What types of dihedral point group do you know?

Section 3

1. What is a matrix?

2. What are the multiplication rules for matrices?

3. Explain why transformation matrices represent symmetry operations?

4. What is an irreducible representation?

5. What is a reducible representation?

6. What is meant by an A and B symmetry type of an irreducible representation?

7. Explain briefly, why there are non-zero entries on positions other than those on the trace of the matrix for C₃ symmetry operations?

8. The x and y coordinates are dependent for C₃ rotations around the z axis in the point group C_3v. Explain.

9. The irreducible representation of the type E contains characters other than +1 and -1. Explain how these characters are generated?

10. Two orbitals are degenerate when a symmetry operation can interconvert them. Show how the double degeneracy of the 2p_x and the 2p_y orbitals in the point group C_3v can be demonstrated using this principle.

Dr. Kai Landskron (Lehigh University). If you like this textbook, please consider to make a donation to support the author's research at Lehigh University: Click Here to Donate.