En anglais

Reading a character table

Science · Chemistry · ages 19-20

Name ______________________ Date ____________

What does each operation-class column of a character table identify?
- A measured vibrational frequency
- A class of symmetry operations
- An element's atomic mass in the molecule
In a character table, what does each character row describe?
- One irreducible symmetry type
- One measured vibrational frequency
- One molecule's complete atomic structure
Acetylene, C2H2, is linear and has four atoms. How many vibrational modes does it have? Count degenerate modes separately.
Answer: ______________
For formaldehyde in C2v, Γ3N=4A1+A2+3B1+4B2. Translations are A1+B1+B2; rotations are A2+B1+B2. Which vibrational symmetry content remains?
- 4A1 + A2 + 3B1 + 4B2
- 3A1 + A2 + 2B1 + 3B2
- 3A1 + B1 + 2B2
Formaldehyde lies in the yz plane. Reflection in xz fixes C and O and exchanges the two H atoms. What is Γ3N's character for this reflection?
Answer: ______________
A C2v normal mode has B2 symmetry. Its table lists y and yz in that row. Which activities are allowed for its fundamental under electric-dipole infrared and first-order Raman rules?
- Infrared, but no first-order Raman activity
- Infrared and first-order Raman
- First-order Raman, but no infrared activity
Use C2v order E,C2,σv(xz),σv(yz). Rows: A1=(1,1,1,1), A2=(1,1,-1,-1), B1=(1,-1,1,-1), B2=(1,-1,-1,1). Reducing Γ=(4,0,0,0) gives A1+A2+B1+B2.
Circle one: True False
A molecule has an inversion centre. One normal mode is electric-dipole infrared active. What is the first-order Raman activity of that same mode?
- Inactive by mutual exclusion
- Equally active because every infrared mode is Raman active
- Active only at a higher frequency than its infrared band

Answer key

For grown-ups. Fold this page away before handing over the rest.

Reading a character table W1-mt_L8cTQjeKwf-s1

A class of symmetry operations · Character columns identify operation classes. Separate function columns may list coordinates, rotations or quadratic functions.
One irreducible symmetry type · Each row is an irreducible representation. Its characters describe that symmetry type under operation classes.
7 · For a linear molecule, 3N - 5 = 3 x 4 - 5 = 7 vibrational modes.
3A1 + B1 + 2B2 · Subtract both external-motion sets coefficient by coefficient. The remainder is 3A1+B1+2B2, representing six one-dimensional modes.
2 · Two atoms remain fixed, each contributing mirror trace +1. The exchanged hydrogens contribute zero, giving 2 x 1 = 2.
Infrared and first-order Raman · The coordinate y permits infrared activity. The quadratic function yz permits first-order Raman activity. Neither permission guarantees a detectable peak.
True · Each row has identity character 1. Every product sum is 4, and dividing by the four operations gives one copy of each row.
Inactive by mutual exclusion · Mutual exclusion forbids both activities for the same mode. It does not exclude a different Raman-active mode at a coincident frequency.