Diffraction Effects of Momentum (AQA AS Physics)

• When electrons pass through a slit similar in size to their de Broglie wavelength, they exhibit diffraction, a property of waves
• The regular spacing of atoms in a crystalline solid acts 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:

• 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)

Comparison of electron diffraction patterns at different values of momentum

Momentum of electrons

• 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 of electrons

• The speed of an electron can be increased by increasing the accelerating voltage (or potential difference)
• If the electron speed, and therefore kinetic energy is increased, 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 shorter its de Broglie 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