IB DP Physics: HL复习笔记12.1.5 Matter Waves

Matter Waves

  • De Broglie proposed that electrons travel through space as a wave
    • This would explain why they can exhibit behaviour such as diffraction
  • He therefore suggested that electrons must also hold wave properties, such as wavelength
    • This came to be known as the de Broglie wavelength
  • However, he realised all particles can show wave-like properties, not just electrons
    • He hypothesised that all moving particles have a matter wave associated with them
  • This is known as the de Broglie wavelength, and can be defined as:

The wavelength associated with a moving particle

  • The majority of the time, and for everyday objects travelling at normal speeds, the de Broglie wavelength is far too small for any quantum effects to be observed
    • A typical electron in a metal has a de Broglie wavelength of about 10 nm
  • Therefore, quantum mechanical effects will only be observable when the width of the sample is around that value

Electron-Diffraction-Experiment

  • The electron diffraction tube can be used to investigate how the wavelength of electrons depends on their speed
    • The smaller the radius of the rings, the smaller the de Broglie wavelength of the electrons
  • As the voltage is increased:
    • The energy of the electrons increases
    • The radius of the diffraction pattern decreases
  • This shows as the speed of the electrons increases, the de Broglie wavelength of the electrons decreases
  • 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:Kinetic Energy 
  • Since kinetic energy E = ½ mv2
  • Momentum and kinetic energy can be related by:
  • 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 ExampleMass 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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