The de Broglie Wavelength (AQA AS Physics)

• The de Broglie equation relates wavelength (a property of waves) to momentum (a property of matter)

• In the electron diffraction experiment:
  • Increasing the speed of electrons, and hence their momentum, causes the angle of diffraction to decrease (as seen by the decrease in the diameter of the diffraction rings)

• This is in agreement with wave theory, where the angle of diffraction decreases as the wavelength decreases
  • Therefore, the greater the momentum of the particle, the smaller the de Broglie wavelength

• Using ideas based on 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:

• Using momentum , the de Broglie wavelength can be written in terms of the speed of a moving particle:

• Using kinetic energy , momentum and kinetic energy can be related by:

Energy:   

Momentum: 

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

• 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)