AQA A Level Physics

Revision Notes

2.5.4 The de Broglie Wavelength

The de Broglie Wavelength

  • Using ideas based upon the quantum theory and Einstein’s theory of relativity, de Broglie suggested that the momentum (p) of a particle and its associated wavelength (λ) are related by the equation:

Calculating de Broglie Wavelength equation 1

  • Since momentum p = mv, the de Broglie wavelength can be related to the speed of a moving particle (v) by the equation:

Calculating de Broglie Wavelength equation 2

  • Since kinetic energy E = ½ mv2
  • Momentum and kinetic energy can be related by:

Calculating de Broglie Wavelength equation 3

  • Combining this with the de Broglie equation gives a form which relates the de Broglie wavelength of a particle to its kinetic energy:

Calculating de Broglie Wavelength equation 4

  • Where:
    • λ = the de Broglie wavelength (m)
    • h = Planck’s constant (J s)
    • p = momentum of the particle (kg m s-1)
    • E = kinetic energy of the particle (J)
    • m = mass of the particle (kg)
    • v = speed of the particle (m s-1)

Worked Example

A proton and an electron are each accelerated from rest through the same potential difference. Determine the ratio:

Mass of a proton = 1.67 × 10–27 kg

Mass of an electron = 9.11 × 10–31 kg

2.5.4 De Broglie Wavelength Worked Example

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