4.11.5 The de Broglie Equation

• Using ideas based upon the quantum theory and Einstein’s theory of relativity, de Broglie related the momentum of a particle to its wavelength
• This is known as the de Broglie equation:

• Where:
  • λ = the de Broglie wavelength (m)
  • h = Planck's Constant (J s)
  • p = momentum (kg m s^-1)

• The de Broglie equation, therefore, links a particle-like property (momentum) to a wave-like property (wavelength) demonstrating wave-particle duality for all particles
• Since momentum p = mv, the de Broglie wavelength can be related to the speed of a moving particle (v) by the equation:

• Since kinetic energy E is equal to

 E = ½ mv²

• Momentum and kinetic energy can be related by:

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

• Where:
  • E = kinetic energy of the particle (J)
  • m = mass of the particle (kg)
  • v = speed of the particle (m s^-1)