De Broglie's Hypothesis

• What is De Broglie's hypothesis about particles?

  Particles can behave like waves and particles
• How did De Broglie derive his equation for photon momentum?

  By equating two equations from Einstein
• What is the equation for the energy of a photon?

  E = hf
• What does the equation mc^2 represent?

  The energy of a particle with mass
• What does the symbol h represent in De Broglie's equations?

  Planck's constant
• What does the symbol c represent in De Broglie's equations?

  The speed of light
• What is the relationship between momentum p and wavelength λ according to De Broglie?

  p = h/λ
• How can De Broglie's hypothesis be applied to accelerated electrons?

  To find their wavelength using momentum
• What is the equation relating work done on an electron by an electric field to its kinetic energy?

  eV = 1/2 mv^2
• How do you find the speed of an electron from the work done on it?

  v = $\sqrt{\frac{2eV}{m}}$
• What happens to the wavelength of an electron as eV increases?

  Wavelength λ decreases
• How do you find the wavelength of an accelerated electron?

  • Use the equation: λ = h / (2meV)
  • Substitute the electron's momentum
  • Relate it to the work done by the electric field
• What is the new wavelength of an electron if the potential difference increases by a factor of 25?

  λ' = λ/5
• Why does the new wavelength of the electron decrease when the potential difference increases?

  Because the electron moves faster
• What algebraic skills are important for manipulating De Broglie's equations?

  • Confidence in algebra involving square roots
  • Ability to combine square roots
  • Understanding of manipulating equations