Molecular Motion Quantised: The Oscillator and the Rotor · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Springs and dumbbells: how molecules move

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

  1. At absolute zero a bond sits perfectly still with no energy.

    Circle one:   True   False

  2. How are vibrational levels spaced, and rotational levels?

    • Both ladders are evenly spaced
    • Vibration is even, rotation widens with J
    • Vibration widens with J, rotation is even

  3. What connects the moment of inertia to the bond length?

    • I = mu r squared, with mu the reduced mass
    • I equals the frequency times the bond length
    • I equals the number of vibrational levels

  4. Which change raises a vibrational frequency?

    • A stiffer bond at the same mass
    • A heavier atom at the same stiffness
    • A longer bond at the same stiffness

  5. You know the vibrational frequency of H-Cl. What changes for D-Cl, and which way does the band move?

    • The stiffness changes and the band moves up
    • Nothing changes because the bond is identical
    • The reduced mass grows and the band moves down

  6. Rotational gaps run 2B, 4B, 6B. What comes next?

    • 7B
    • 6B again
    • 8B

  7. Two rotors have equal masses, but A shows wider line spacing than B. What follows?

    • A has the longer bond
    • A has the shorter bond
    • Both bonds must be identical

  8. A student says a bond at absolute zero sits perfectly still. What is the error?

    • The bond breaks apart at absolute zero
    • The half quantum at v = 0 keeps it moving
    • Rotation stops but vibration doubles instead
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Answer key

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

Springs and dumbbells: how molecules move W1-mt_dHgi-i9pxc-s1

  1. False · The half quantum at v = 0 never goes away.
  2. Vibration is even, rotation widens with J · Springs climb evenly, dumbbells spread wider as they spin faster.
  3. I = mu r squared, with mu the reduced mass · One equation turns a spinning measurement into a distance.
  4. A stiffer bond at the same mass · Frequency rises with stiffness and falls with mass.
  5. The reduced mass grows and the band moves down · Same spring, heavier mass, lower note.
  6. 8B · The dumbbell ladder keeps spreading wider with J.
  7. A has the shorter bond · Wider spacing means larger B, smaller I, shorter r.
  8. The half quantum at v = 0 keeps it moving · Zero point energy forbids perfect stillness.
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