AQA A Level Physics复习笔记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:

4.-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:

4.-Calculating-de-Broglie-Wavelength-equation-2

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

4.-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:

4.-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:

 

转载自savemyexams

 

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