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Wave-Particle Duality

The de Broglie wavelength

  • 3 things to know
  • Unit AS 2

Overview

De Broglie equation, defining every symbol with its unit and de Broglie's hypothesis.

What you need to know

Answer each one before you reveal it.

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Key term

State the de Broglie equation, defining every symbol with its unit.

Key term

How does the de Broglie relation apply to photons?

Key term

Why can an electron microscope resolve much finer detail than a light microscope?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the de Broglie equation, defining every symbol with its unit.

    Model answer

    λ = h/mv, where λ is the de Broglie wavelength in metres, h is the Planck constant in J s, m is the mass of the particle in kg and v is its speed in m s⁻¹.

  2. 2

    Write the de Broglie equation in terms of momentum.

    Model answer

    λ = h/p, where p is the momentum of the particle in kg m s⁻¹ and h is the Planck constant in J s.

  3. 3

    State de Broglie's hypothesis.

    Model answer

    De Broglie proposed that every moving particle has an associated wavelength given by the Planck constant divided by its momentum, so that matter as well as radiation shows wave-particle duality.

  4. 4

    Why is the wavelength associated with a moving particle called its de Broglie wavelength?

    Model answer

    It is named after de Broglie, who first suggested that the relation λ = h/p already known for photons should apply to particles with mass as well.

  5. 5

    What happens to the de Broglie wavelength of a particle as its speed increases?

    Model answer

    The wavelength decreases, because it is inversely proportional to the momentum and therefore to the speed for a given mass.

  6. 6

    What happens to the de Broglie wavelength of particles of the same speed as their mass increases?

    Model answer

    The wavelength decreases in inverse proportion to the mass, which is why heavier particles show wave behaviour far less readily.

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