The photoelectric effect reveals light's particle-like nature. When light hits a metal, it can kick out electrons, but only if it has enough energy. This energy depends on light's frequency, not its brightness.

Understanding the photoelectric effect is crucial for grasping quantum mechanics. It shows how light behaves as both a wave and a particle, challenging classical physics and paving the way for modern quantum theory.

The Photoelectric Effect

Photoelectric effect and light particles

• Light behaves as discrete particles called photons
  • Each photon carries a specific amount of energy determined by its frequency (visible light, ultraviolet)
  • Photons interact with electrons in a metal surface (gold, zinc), causing them to be ejected as photoelectrons
• Increasing light intensity increases the number of electrons ejected but does not increase their kinetic energy
  • More photons interact with more electrons, resulting in a greater number of ejected electrons
  • This suggests that individual photons are responsible for ejecting electrons, not the overall intensity of light
• A minimum frequency of light is required to eject electrons from a metal surface
  • This threshold frequency is specific to the metal and is related to its work function (energy needed to remove an electron)
  • Below this frequency, no electrons are ejected regardless of light intensity (infrared light)
  • This supports the idea that photons must have a minimum energy to overcome the work function and eject electrons

Energy calculations for photons

• The energy of a photon $E$ is directly proportional to its frequency $f$
  • $E = hf$, where $h$ is Planck's constant $6.626 \times 10^{-34}$ J$\cdot$s
• Photon energy is inversely proportional to its wavelength $\lambda$
  • $E = \frac{hc}{\lambda}$, where $c$ is the speed of light $3.0 \times 10^8$ m/s
• To calculate photon energy from frequency:
  1. Multiply the frequency by Planck's constant
  2. Example: A photon with a frequency of $6.0 \times 10^{14}$ Hz has an energy of $E = 6.626 \times 10^{-34}$ J$\cdot$s \times 6.0 \times 10^{14}$ Hz $= 3.98 \times 10^{-19}$ J
• To calculate photon energy from wavelength:
  1. Divide the product of Planck's constant and the speed of light by the wavelength
  2. Example: A photon with a wavelength of 500 nm has an energy of $E = \frac{6.626 \times 10^{-34} \text{ J} \cdot \text{s} \times 3.0 \times 10^8 \text{ m/s}}{500 \times 10^{-9} \text{ m}} = 3.98 \times 10^{-19}$ J

Light properties in photoelectric effect

• Changing light frequency affects the kinetic energy of ejected electrons
  • If the frequency is above the threshold frequency (ultraviolet light), increasing it will increase the kinetic energy of ejected electrons
  • If the frequency is below the threshold frequency (infrared light), no electrons will be ejected regardless of the intensity
• Changing light intensity affects the number of electrons ejected
  • Increasing intensity (brighter light) will increase the number of photons incident on the metal surface
  • More photons will interact with more electrons, causing a greater number of electrons to be ejected
  • However, increasing intensity does not change the kinetic energy of individual ejected electrons
• The maximum kinetic energy $KE_{max}$ of ejected electrons is related to the photon energy and the metal's work function $\phi$
  • $KE_{max} = hf - \phi$
  • If the photon energy $hf$ is greater than the work function, the excess energy is converted into the kinetic energy of the ejected electron
  • If the photon energy is less than the work function, no electrons will be ejected (red light on zinc)

Experimental setup and measurements

• The photoelectric effect is typically studied using a cathode-anode system in a vacuum tube
  • The cathode is the metal surface from which electrons are ejected
  • The anode collects the ejected electrons, creating a measurable current
• A stopping potential can be applied to measure the maximum kinetic energy of ejected electrons
  • This is the minimum voltage needed to prevent any electrons from reaching the anode
  • The stopping potential is directly related to the maximum kinetic energy of the photoelectrons
• Electromagnetic radiation, such as visible light or X-rays, is used to induce the photoelectric effect
  • Different types of radiation have varying frequencies and energies, affecting their ability to eject electrons from the metal surface