de Broglie Waves and Electron Diffraction · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

When particles behave like waves

Science · Waves, Light & Sound · ages 17-18
Name ______________________   Date ____________

  1. An electron's momentum doubles while h stays fixed. What happens to its wavelength?

    • It doubles
    • It halves
    • It stays the same

  2. Which observation proves that electrons behave as waves?

    • Light casting sharp shadows
    • Rings from electrons through graphite
    • Echoes bouncing off a wall

  3. A flying cricket ball has a wavelength far too tiny to ever show diffraction.

    Circle one:   True   False

  4. A 0.05 kg tennis ball moves at 20 m/s. Its de Broglie wavelength is about 6.6e-34 m, far too small to notice.

    Circle one:   True   False

  5. The accelerating voltage is raised from 100 V to 900 V. What happens to the electron's de Broglie wavelength?

    • It falls to one third
    • It falls to one ninth
    • It grows three times
    • It stays the same

  6. An electron is accelerated from rest through 600 V. Take e = 1.6e-19 C, m = 9.11e-31 kg and h = 6.63e-34 J s. Find its de Broglie wavelength in units of 10^-11 m, to 2 significant figures.

    Answer: ______________

  7. Electrons diffract through graphite into rings. The voltage is raised. What happens to the rings?

    • They grow wider
    • They vanish at once
    • They shrink inward

  8. Electron diffraction rings from graphite shrink when the accelerating voltage is raised. Why?

    • Electron waves get shorter and bend less
    • The graphite crystal shrinks as it heats
    • Fewer electrons reach the screen
    • Slower electrons spread out less

  9. Ben expects electron diffraction at a wide open doorway. Why will he see nothing?

    • The gaps must be near atomic size
    • Electrons move too slowly to diffract
    • Crystals absorb every electron

  10. The accelerating voltage drops to one quarter of its value. What happens to the wavelength?

    • It doubles
    • It halves
    • It stays the same
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Answer key

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

When particles behave like waves W1-mt_Y8NthsmPcv-s1

  1. It halves · Wavelength is h over momentum, so twice the bottom means half the wavelength.
  2. Rings from electrons through graphite · Diffraction rings need interfering waves, and the electrons draw them.
  3. True · Its huge momentum makes its wavelength absurdly smaller than any object it meets.
  4. True · Its momentum is 0.05 x 20 = 1.0 kg m/s, so its wavelength is 6.63e-34 / 1.0, about 6.6e-34 m. No gap is anywhere near that small.
  5. It falls to one third · The voltage rises 9 times, momentum rises by the square root of 9, which is 3, so the wavelength falls to one third.
  6. 5 · E = 1.6e-19 x 600 = 9.6e-17 J, p = square root of (2 x 9.11e-31 x 9.6e-17), about 1.32e-23 kg m/s, so the wavelength is 6.63e-34 / 1.32e-23 = 5.0e-11 m.
  7. They shrink inward · Higher voltage shortens the wavelength, and shorter waves bend through smaller angles.
  8. Electron waves get shorter and bend less · A higher voltage gives more momentum and a shorter wavelength, and shorter waves bend through smaller angles, so the rings close in.
  9. The gaps must be near atomic size · Electron wavelengths sit near 1e-10 m, so only atomic-scale gaps can reveal them.
  10. It doubles · Momentum follows the square root of voltage, so quarter voltage halves momentum and doubles wavelength.
Worksheet · LightMySky