ASPhysicsEdexcelRevision Notes5. Waves & Particle Nature of LightWaves, Electrons & Photons5.29 The de Broglie Equation

The de Broglie Equation (Edexcel AS Physics)

Revision Note

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Lindsay Gilmour

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The de Broglie Equation

  • Using ideas based upon the quantum theory and Einstein’s theory of relativity, de Broglie theorised that not only do EM waves sometimes behave as particles, but that very small, fast moving particles like electrons could also behave as waves
    • He called these matter waves
  • The Broglie equation relates the wavelength of some particles to their mass and velocity, which combine to give their momentum
    • Hence:

lambda equals fraction numerator h over denominator m v end fraction equals h over p

    • λ = the de Broglie wavelength (m)
    • h = Planck's Constant (J s)
    • m = mass (kg)
    • v = velocity (m s-1)
    • p = momentum (kg m s-1)

Worked example

Determine the de Broglie wavelength of a person of mass 70 kg moving at 2 ms-1 and comment on your answer.

Step 1: Write the known values

    • Mass, m = 70 kg
    • Velocity, v = 2 m s−1
    • Planck's constant, h = 6.63 × 10−34 Js

Step 2: Write the equation and substitute the values

lambda equals fraction numerator h over denominator m v end fraction equals fraction numerator left parenthesis 6.63 space cross times space 10 to the power of negative 34 end exponent right parenthesis over denominator 70 space cross times space 2 end fraction space equals space 4.74 space cross times space 10 to the power of negative 36 end exponent

Step 4: Write the answer to the correct number of significant figures and include units

    • de Broglie wavelength of a moving person, λ = 4.7 × 10−36 m

Step 5: think about the magnitude of the result and comment on it

    • The person does have a de Broglie wavelength but since it is about 1020 times smaller than a nucleus, it can be ignored
    • People behave like particles, not waves

Examiner Tip

If you've not been given the mass of a particle in a question, make sure to look at your data sheet which includes the rest mass of various particles

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    Lindsay Gilmour

    Author: Lindsay Gilmour

    Expertise: Physics

    Lindsay graduated with First Class Honours from the University of Greenwich and earned her Science Communication MSc at Imperial College London. Now with many years’ experience as a Head of Physics and Examiner for A Level and IGCSE Physics (and Biology!), her love of communicating, educating and Physics has brought her to Save My Exams where she hopes to help as many students as possible on their next steps.