All subjects · Physics · WPH12 (Unit 2)

Electron diffraction and the de Broglie wavelength

Light can behave like particles, and particles such as electrons can behave like waves. Electron diffraction is the evidence.

Electron diffraction

A beam of electrons is accelerated and fired at a thin layer of graphite. A pattern of bright rings appears on a fluorescent screen. Diffraction is a wave property, so this is evidence that electrons behave as waves. It works because the spacing of carbon atoms is similar to the electrons' wavelength.

The de Broglie equation

Any particle with momentum p has a wavelength λ = h / p = h / mv, where h = 6.63 x 10-34 J s is the Planck constant. Larger momentum means a shorter wavelength.

Changing the pattern

Increasing the accelerating voltage makes the electrons faster, so their momentum rises and their wavelength falls. The rings get smaller (less diffraction). Everyday objects have huge momentum compared with electrons, so their wavelengths (around 10-34 m) are far too small to show diffraction.

Worked example

Find the de Broglie wavelength of an electron moving at 2.0 x 106 m/s.

  1. p = mv = 9.11 x 10-31 x 2.0 x 106 = 1.82 x 10-24 kg m/s
  2. λ = h / p = 6.63 x 10-34 / 1.82 x 10-24

Answer: λ = 3.6 x 10-10 m (0.36 nm)

Key idea: Electron diffraction shows electrons act as waves; λ = h/p = h/mv.

Check yourself

  1. Find the de Broglie wavelength of an electron moving at 4.0 x 106 m/s, in nm, to 3 s.f.
    Show answer

    0.182 nm. λ = 6.63 x 10-34 / (9.11 x 10-31 x 4.0 x 106) = 1.82 x 10-10 m = 0.182 nm.

  2. An electron has a de Broglie wavelength of 1.0 x 10-10 m. Find its speed, in units of 106 m/s, to 3 s.f.
    Show answer

    7.28 x 106 m/s. v = h / (mλ) = 6.63 x 10-34 / (9.11 x 10-31 x 1.0 x 10-10) = 7.28 x 106 m/s.

  3. An electron has a de Broglie wavelength of 0.20 nm. Its speed is doubled. Find its new wavelength in nm.
    Show answer

    0.1 nm. λ ∝ 1/v, so doubling v halves λ: 0.10 nm.

  4. Electron diffraction is evidence that
    • electrons have negative charge
    • light is made of photons
    • electrons can behave as waves
    • electrons have mass
    Show answer

    electrons can behave as waves. Diffraction is a wave behaviour.

  5. The accelerating voltage in an electron diffraction tube is increased. What happens to the rings?
    • They get smaller
    • They get larger
    • They disappear
    • They do not change
    Show answer

    They get smaller. Faster electrons have shorter wavelengths, so they diffract less.

  6. An electron and a proton move at the same speed. Which has the longer de Broglie wavelength?
    • The proton
    • They are equal
    • The electron
    • Neither has a wavelength
    Show answer

    The electron. The electron has much less mass, so less momentum and a longer λ.

  7. Why does a moving tennis ball not show diffraction effects?
    • Its de Broglie wavelength is far too small compared with any gap
    • It has no momentum
    • It is not charged
    • Only electrons have a wavelength
    Show answer

    Its de Broglie wavelength is far too small compared with any gap. Its large momentum gives λ of around 10-34 m, much smaller than any gap or obstacle.

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Last updated 7 November 2026. Spotted a mistake? Tell us.