Diffraction Effects of Momentum (AQA A Level Physics): Revision Note

Diffraction effects of momentum

• 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:

$\lambda =\frac{h}{mv}$

• Where:

  • $\lambda$ = 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)

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