Character Tables and What Symmetry Predicts · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading a character table

Science · Chemistry · ages 19-20
Name ______________________   Date ____________

  1. 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

  2. In a character table, what does each character row describe?

    • One irreducible symmetry type
    • One measured vibrational frequency
    • One molecule's complete atomic structure

  3. Acetylene, C2H2, is linear and has four atoms. How many vibrational modes does it have? Count degenerate modes separately.

    Answer: ______________

  4. 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

  5. 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: ______________

  6. 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

  7. 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

  8. 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
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Answer key

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

Reading a character table W1-mt_L8cTQjeKwf-s1

  1. A class of symmetry operations · Character columns identify operation classes. Separate function columns may list coordinates, rotations or quadratic functions.
  2. One irreducible symmetry type · Each row is an irreducible representation. Its characters describe that symmetry type under operation classes.
  3. 7 · For a linear molecule, 3N - 5 = 3 x 4 - 5 = 7 vibrational modes.
  4. 3A1 + B1 + 2B2 · Subtract both external-motion sets coefficient by coefficient. The remainder is 3A1+B1+2B2, representing six one-dimensional modes.
  5. 2 · Two atoms remain fixed, each contributing mirror trace +1. The exchanged hydrogens contribute zero, giving 2 x 1 = 2.
  6. 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.
  7. True · Each row has identity character 1. Every product sum is 4, and dividing by the four operations gives one copy of each row.
  8. 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.
Worksheet · LightMySky