4.5 Quantum physics

• Photon - a 'particle of light' or a quantum of electromagnetic charge
• E=hf = hC/$\lambda$

  E - energy of a proton

  h - Planck's constant (6.63 *10^-34)

  f - frequency

  C - speed of light in a vacuum

  λ - wavelength
• The electronvolt is the energy transferred to or from one electron when it moves through a potential difference of 1V
• The threshold voltage is the minimum potential difference at which a diode begins to conduct
• Energy of a photon is inversely proportional to its wavelength
• E = VQ

  E - energy

  V - potential difference

  Q - charge
• Threshold voltage is inversely proportional to wavelength

  $V =$$hC/e\lambda =$$hf/e$
• Photoelectric effect - the emission of photoelectrons from a metal surface when electromagnetic radiation above a threshold is incident on the metal
• Photoelectrons are electrons emitted from the surface of a metal by the photoelectric effect
• Key observations from the photoelectric effect experiment

  1. Incident radiation had to be above a certain frequency - intensity did not matter if the frequency was less than the fundamental
  2. Emission of photoelectrons was instantaneous when the frequency exceeded the threshold frequency
  3. Intensity did not affect the kinetic energy of the electrons, but the number of electrons emitted. Increased frequency would increase the kinetic energy of electrons
• The photoelectric effect cannot be explained by the wave model of light as energy doesn't depend on intensity of radiation (wave behaviour - think EM waves) but instead depends on frequency
• The photon model better explains the photoelectric effect - each electron in the metal surface must require a certain amount of energy in order to escape the metal and that each photon could transfer its exact energy to one surface electron in a one-to-one interaction
• Increasing frequency increases photoelectron kinetic energy as energy of a photon depends on frequency, not intensity. If a photon does not carry enough energy on its own to free an electron the number of photons makes no difference as it is a one-to-one interaction
• There is no time delay in photoelectron emission as electrons cannot accumulate energy from multiple photons - if the incident radiation is greater than the threshold frequency, photoelectrons are immediately released as photons hit the surface
• The work function, $\phi$, measured in joules, is the minimum energy needed to remove a single electron from the surface of a particular metal
• The threshold frequency is the minimum frequency of the EM radiation that will cause the emission of an electron from the surface of a particular metal
• increasing frequency increases the kinetic energy of photoelectrons
• Increasing intensity increases photoelectron emission if the frequency is above the threshold frequency as more photons with the same kinetic energy are emitted
• Einstein's photoelectric effect equation

  $hf=$$\phi+$$KE_{max}$

  h - planck constant

  f - frequency

  $\phi$ - work function; minimum energy required to free a single electron form the metal surface

  $KE_{\max}$ - maximum kinetic energy of the emitted electron
• Einstein's photoelectric effect equation is a statement of the conservation of energy as only a single electron is emitted from a one-to-one interaction and any remaining energy is transferred into the kinetic energy of the photoelectron
• Some electrons require more energy than the work function to be freed from the metal as they are closer to the metal ions than others

  The work function is the minimum energy, but most electrons require a little more energy
• If a photon strikes the surface of the metal at the threshold frequency, then there is only enough energy to free it from the surface, and it would have a kinetic energy of 0J
• The de Broglie equation

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

  $\lambda$ - wavelength

  h - planck constant

  p - momentum of the particle
• Wave-particle duality - a theory that states that matter has both particle and wave properties
• Wave properties are often not seen in larger particles as they become harder to observe - often almost undetectable as wavelength is so small due to greater mass
• Electrons behave as a wave when they diffract around thin pieces of crystalline graphite

  Electrons behave as particles in the photoelectric effect and in Milikan's oil drop experiment
• Wave nature of electrons is hard to observe as it requires a very tiny gap to observe the diffraction as they have a very small wavelength