AQA A Level Physics复习笔记2.5.5 Diffraction Effects of Momentum

Diffraction Effects of Momentum

 

  • When electrons pass through a slit similar in size to themselves, they exhibit a wavelike property( Diffraction), meaning they spread out like a wave passing through a narrow gap
  • The regular spacing of atoms in a crystalline solid act as a diffraction grating, scattering the electrons in a predictable manner
  • The observed diffraction pattern can be used to deduce the structure of the crystal producing that pattern
  • High energy electrons have a shorter wavelength and can therefore be used to look at the size of the nucleus of an atom as opposed to the arrangement of atoms in a crystal
  • The de Broglie wavelength tells us about the wave-particle relationship:

2.5.5-De-Broglie-Wavelength-Equation-

  • Where:
    • λ = the de Broglie wavelength (m)
    • h = Planck’s Constant (J s)
    • m = mass of the electron (kg)
    • v = velocity of the electron (m s–1)

     

 

Diffraction-Effects-of-Momentum

Comparison of electron diffraction patterns at different values of momentum

 

Momentum

  • Momentum is equal to p = mv, so, from de Broglie's equation:
    • A smaller momentum will result in a longer wavelength
    • A larger momentum will result in a shorter wavelength

     

Kinetic Energy

  • If the electron speed / kinetic energy is increased, by increasing the accelerating voltage, then:
    • The wavelength of the wave will decrease
    • The diffraction rings will appear closer together

     

  • The higher the kinetic energy of the electron, the higher its momentum hence the smaller its wavelength

Radius of the Diffraction Pattern

  • The radius of the diffraction pattern depends on the wavelength:
    • The longer the wavelength, the more the light spreads out hence a larger radius is produced
    • The shorter the wavelength, the smaller the radius produced

     

  • Therefore, electrons with smaller momentum will produce a more diffuse diffraction pattern

 

转载自savemyexams

 

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