Threshold Frequency & Work Function

• The Threshold Frequency involves the photoelectric effect.

  This is a phenomenon where electrons are emitted from the surface of a metal when it absorbs electromagnetic radiation.
• Electrons removed from the metal are named photoelectrons.

  The photoelectric effect shows evidence of how light behaves as a particle.

  Light is quantised or carried in packets called photons.

  
  

  This is because each electron can absorb only one photon. So only frequencies of light above a threshold frequency can emit photoelectrons
• The threshold frequency is:

  • The minimum frequency of incident electromagnetic radiation required to move a photoelectron from the surface of a metal
• The threshold wavelength:

  • The longest wavelength of incident electromagnetic radiation that can just remove a photoelectron from the surface of a metal, corresponding to the minimum energy required to overcome the metal's work function.
• The work function Φ or threshold energy, of a material is:

  The minimum energy to release a photoelectron from the surface of a metal.
• Imagine the electrons being in an energy well inside the metal.

  The walls as different energy levels.

  The surface of the well where the electrons reside.

  And the top of the well is the energy level required for the electron to overcome to escape the metal.

  
• Alkali metals such as sodium and potassium have threshold frequencies in the visible light region

  .

  because the attractive forces between the surface electrons and positive metal ions are relatively weak
• Transition metals such as zinc and iron have threshold frequencies in the ultraviolet region.

  .

  This is because the attractive forces between the surface electrons and positive metal ions are much stronger
• Stopping Potential Vs is defined as:

  • The potential difference required to stop the photoelectron emission from ocurring
• The collector plate is the plate where electrons cross a gap from the emitter plate

  
• The metal plate that emits photoelectrons when photos arrive on it is called the Emitter plate

  
• To find the maximum kinetic energy of emitted photoelectrons:

  • Find the highest point in which the photoelectrons can't pass to the collector plate
  • The flow of electrons across the gap results in an electromotive force between the plates that cause current to flow around.
  • It becomes a photoelectric cell making a photoelectric current
• If the e.m.f of the variable power supply is initally zero, that means the circuit only operates on the photoelectric current.

  • E.M.F means the energy provided by an electrical source of power
• What happens to the emitter plate as the power supply is turned up?

  It becomes more positive
• Why are electrons attracted back to the emitter plate?

  Because they are negatively charged and opposites attract
• What happens to electrons that escape the emitter plate?

  They go to the collector plate
• What effect does increasing the e.m.f of the supply have?

  It increases the potential difference
• What is the stopping potential denoted as?

  Vs
• What occurs when the potential difference is so high that no electrons can cross the gap?

  This is known as the stopping potential
• What does the energy to cross the gap equal at the stopping potential?

  It equals the maximum kinetic energy of the electrons
• What happens if electrons have more kinetic energy than the maximum at the stopping potential?

  They can cross the gap
• The equation for maximum kinetic energy of photoelectrons is:

  .

  $E_{k_{\text{max}}} =$$eV_s$

  • Ekmax = Maximum kinetic energy of photoelectrons
  • e = Charge on electron
  • Vs = stopping potential
• Increasing the intensity of the incident radiation increases:

  • The number of photons incident on the metal plate
  • The number of photoelectrons emitted from the plate. (the photoelectric current)

  For given potential difference, increasing the intensity, increases the photoelectric current but the stopping potential stays the same.

  This shows that intensity doesn't affect the kinetic energy of the photoelectrons
• The maximum kinetic energy of the photons (and photoelectrons) depend on:

  • The frequency (or wavelength) of the incident photons.
  • The work function of the metal.

  However, if the frequency or wavelength is changed while the intensity is constant the photoelectric current won't be constant.
• Increasing the frequency of the incident radiation while keeping the intensity constant will make the photoelectric current decrease because there will be fewer photons for the same intensity. Since each photon has more energy, the total energy is divided among fewer photons, leading to fewer emitted electrons.
• Keeping the intensity of the incident radiation constant means,

  • Energy transferred per unit area is the same
  • So a higher frequency source will emit fewer photons per unit area since higher frequency photons carry more energy. So lower frequency = more photons per area.
  • If there are fewer photons incident on a given area every second, the number of electrons emitted will decrease.
• This is the graph:

  High intensity vs Low intensity

  
• The stopping potential remains constant at different intensities of incident radiation, showing that the intensity of light does not affect the maximum kinetic energy of photoelectrons, but only the number of photoelectrons emitted.
• In a photoelectric effect setup, there's two plates.

  • Emitter plate (Cathode)
  • Releases electrons and is normally neutral or positive.
  • Light is shone onto this

  Collector plate (anode):

  • Collects electrons that were emitted
  • Normally positive charge to attract electrons.
  • When measuring stopping potential, A power supply is connected to the anode (negative) and positive at the cathode (positive) to repel the electrons that escape.
  • The minimum potential difference to stop the fastest electrons is the stopping potential.