Symmetry

Question 1

Number of faces on a cube?

Answer 1

6

Question 2

Number of vertices on a cube?

Answer 2

8

Question 3

Number of faces on a tetrahedron?

Answer 3

4

Question 4

Number of faces on an octahedron?

Answer 4

8

Question 5

Number of vertices on a tetrahedron?

Answer 5

4

Question 6

“Procedure to Determine”

C_{<strong>2v</strong>}

Answer 6

“Procedure to Determine”

Not a special group

C_2​ (yes, principal axis)

No ⊥C₂

No σ_h

2σ_v

Question 7

Chiral Point Groups

Answer 7

C_n ,D_{<b>n </b>}T, O, and I groups only

Question 8

All chiral molecules are polar

True or False

Answer 8

False

(e.g. Molecules in the D_n point group are chiral but not polar.)

Question 9

Chiral Molecule

Answer 9

Molecules that lack an improper rotation axis

Question 10

“Procedure to Determine”

C Point Groups

Answer 10

“Procedure to Determine”

Not a special group

No n⊥C₂ to principal axis

Question 11

“Procedure to Determine”

D Point Groups

Answer 11

“Procedure to Determine”

Not a special Group

n⊥C₂ to principal axis

Question 12

“Procedure to Determine”

D_{<strong>5d</strong>}

Answer 12

“Procedure to Determine”

Not a special group

C_5​ (yes, principal axis)

5 ⊥C₂

No σ_h

5σ_d

Question 13

“Procedure to Determine”

C_{<strong>∞​V</strong>}

Answer 13

“Procedure to Determine”

Linear (Yes)

No ⊥C₂

Question 14

“Useful Matrices”

Answer 14

“Useful Matrices”

i

Question 15

“Point Groups”

Bent corresponding point group

Answer 15

C_2v

Question 16

“Point Groups”

SeeSaw corresponding point group

Answer 16

C_2v

Question 17

“Point Groups”

Square Planar corresponding point group

Answer 17

D_4h

Question 18

“Point Groups”

T-Shape corresponding point group

Answer 18

C_2v

Question 19

“Point Groups”

Trigonal Bipyramidal corresponding point group

Answer 19

D_3h

Question 20

“Point Groups”

Trigonal Planar corresponding point group

Answer 20

D_3h (SO₃)

C_2v (Acetone)

C_s (Methyl formate)

Question 21

“Point Groups”

Trigonal Pyramidal corresponding point group

Answer 21

C_3v

Question 22

σ_perp and σ_h are equivalent types of mirror planes?

True or False

Answer 22

False

Question 23

“Matrix Characters”

χ(S₁ )

Answer 23

1

Question 24

“Matrix Characters”

χ(σ )

Answer 24

1

Question 25

“Matrix Characters”

χ(i)

Answer 25

-3

Question 26

“Matrix Characters”

χ(C₃)

Answer 26

0

Question 27

“Matrix Characters”

χ(C₂)

Answer 27

-1

Question 28

“Useful Matrices”

χ (C₂)

Answer 28

“Useful Matrices”

S₄(z)

Question 29

“Useful Matrices”

Answer 29

“Useful Matrices”

σ_h

Question 30

“Useful Matrices”

Answer 30

“Useful Matrices”

C_{<span>n</span>}(x)

Question 31

“Useful Matrices”

Answer 31

“Useful Matrices”

C_{<span>n</span>}(z)

Question 32

“Useful Matrices”

Answer 32

“Useful Matrices”

C_{<span>3</span>}(z)

Question 33

“Useful Matrices”

Answer 33

“Useful Matrices”

C₂(z)

Question 34

“Groups”

C Point Group

Answer 34

“Groups”

No ⊥ C₂ to principal axis

Question 35

“Groups”

D Point Group

Answer 35

“Groups”

Not a special group

n ⊥ C₂ to principal axis

Question 36

Number of vertices in an octahedron

Answer 36

6

Question 37

5 Platonic solids

Answer 37

Question 38

“Operator”

E

Answer 38

“Operation”

The identity operator is the “do nothing” operator. All points remain at their original position.

Question 39

“Operator”

i

Answer 39

“Operation”

Projects each atom through the center of symmetry to its negative xyz position.

Question 40

“Operator”

σ_h

Answer 40

“Operation”

A mirror plane perpendicular to the principal axis.

Question 41

“Operator”

S_n

Answer 41

“Operation”

A combination of Cn followed by σ_perp yields an improper rotation

Question 42

“Operator”

C_n

Answer 42

“Operation”

A n-fold [360º/n] clockwise rotation about an axis

Question 43

Operations with

axial symmetry elements

Answer 43

C_n and S_n

Question 44

operations using a point symmetry element

Answer 44

E and i