Reducible Representations and Predicting Infrared and Raman Activity · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

From symmetry to band count

Science · Chemistry · ages 22-23
Name ______________________   Date ____________

  1. How do you build the reducible picture of the motions?

    • By matching each label to an axis direction
    • By guessing which bonds vibrate fastest
    • By counting unshifted contributions for each move class

  2. What is the first step in predicting the bands of a molecule?

    • Counting the unshifted contributions
    • Assigning the point group from the resting shape
    • Subtracting the translation and rotation labels

  3. A vibration whose label matches x, y, or z absorbs infrared light.

    Circle one:   True   False

  4. After the reduction formula splits the counts, what must you remove to leave the vibrations?

    • The labels of translation and rotation
    • The labels flagged as Raman active
    • The labels with the largest shares

  5. A surviving label matches a quadratic function but no axis. How does that mode show up?

    • Raman active only
    • Infrared active only
    • Silent in both methods

  6. If two candidate shapes predict different band counts, a measured spectrum can favor one of them.

    Circle one:   True   False

  7. A student reports more vibrations than the molecule can have. Which mistake best explains it?

    • Reading the spectrum before assigning the group
    • Forgetting to subtract translation and rotation labels
    • Mixing up Raman active with silent labels

  8. Candidate A predicts 3 vibrations with all 3 infrared active. Candidate B predicts 3 vibrations with only 1 infrared active. The spectrum shows 3 strong infrared bands. Which shape is favored?

    • Candidate B, since fewer active bands means sharper peaks
    • Neither, since both predict the same vibration total
    • Candidate A, since its active count matches the spectrum
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Answer key

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

From symmetry to band count W1-mt_DP4JfkS6c0-s1

  1. By counting unshifted contributions for each move class · Class-by-class counts of what stays put are the raw material.
  2. Assigning the point group from the resting shape · Every later count hangs on the group, so it comes first.
  3. True · Axis matching means the motion changes the dipole moment.
  4. The labels of translation and rotation · Drift and spin of the whole molecule are motions but not vibrations.
  5. Raman active only · Quadratic matching means changing polarizability, which is the Raman condition.
  6. True · Each candidate predicts its own count, and the spectrum votes.
  7. Forgetting to subtract translation and rotation labels · Kept drift-and-spin labels inflate the vibration count.
  8. Candidate A, since its active count matches the spectrum · Only candidate A explains three infrared-active bands.
Worksheet · LightMySky