Diffraction Effects of Momentum

• What phenomenon do electrons exhibit when passing through a slit similar to their de Broglie wavelength?

  Difraction
• How does the regular spacing of atoms in a crystalline solid affect electrons?

  It acts as a diffraction grating, scattering electrons
• What can the observed diffraction pattern of electrons be used to deduce?

  The structure of the crystal producing it
• Why are high energy electrons used to examine the nucleus of an atom?

  They have a shorter wavelength
• What does the de Broglie wavelength formula represent?

  Wave-particle relationship
• What is the formula for the de Broglie wavelength?

  λ = h / mv
• What does 'h' represent in the de Broglie wavelength formula?

  Planck’s Constant
• What does 'm' represent in the de Broglie wavelength formula?

  Mass of the electron
• What does 'v' represent in the de Broglie wavelength formula?

  Velocity of the electron
• How is momentum defined for electrons?

  p = mv
• What is the property of waves that electrons exhibit when passing through a slit similar in size to their de Broglie wavelength?

  Diffraction
• Why does the regular spacing of atoms in a crystalline solid act as a diffraction grating for electrons?

  It scatters the electrons in a predictable manner
• How can the observed diffraction pattern of electrons be used?

  To deduce the structure of the crystal producing the pattern
• What can high energy electrons be used to look at, as opposed to the arrangement of atoms in a crystal?

  The size of the nucleus of an atom
• What does the de Broglie wavelength tell us about the wave-particle relationship?

  It describes the relationship between the wavelength, Planck's constant, mass, and velocity of an electron
• How does the momentum of electrons affect their de Broglie wavelength?

  A smaller momentum results in a longer wavelength, while a larger momentum results in a shorter wavelength
• How does increasing the kinetic energy of electrons affect their wavelength and the diffraction pattern?

  Increasing the kinetic energy decreases the wavelength, causing the diffraction rings to appear closer together

  
• How does the radius of the diffraction pattern depend on the wavelength of the electrons?

  The longer the wavelength, the more the light spreads out, resulting in a larger radius, while the shorter the wavelength, the smaller the radius

  
• How can the angle of the first minimum of the diffraction pattern be calculated?

  1. Determine the kinetic energy gained by the electron through the potential difference
  2. Calculate the speed of the electron using the kinetic energy
  3. Determine the de Broglie wavelength of the electron using the formula: λ = h/mv
  4. Use the diffraction grating equation: d sin θ = nλ, where n = 1 for the first minimum, to calculate the angle θ
• What is the formula for the de Broglie wavelength?

  $\lambda =$$\frac{h}{mv}$
• What is Planck's constant?

  6.63 × 10^-34 J·s
• What is the mass of an electron?

  9.11 × 10^-31 kg
• What are the key factors that determine the de Broglie wavelength of an electron?

  • Planck's constant (h)
  • Mass of the electron (m)
  • Velocity of the electron (v)
• What are the key factors that determine the radius of the diffraction pattern?

  • Wavelength of the electrons
  • The longer the wavelength, the larger the radius
  • The shorter the wavelength, the smaller the radius

  
• What are the key factors that determine the spacing of the diffraction rings?

  • Wavelength of the electrons
  • The longer the wavelength, the more spread out the diffraction rings
  • The shorter the wavelength, the closer together the diffraction rings
• What are the key differences between the function of a scanning electron microscope (SEM) and a transmission electron microscope (TEM)?

  • TEMs produce 2D images, while SEMs produce 3D images
  • TEMs can only be used for living specimens, while SEMs are for non-living samples