Lecture Notes: The Photoelectric Effect

Introduction to Light Behavior

Light exhibits dual characteristics:
- Acts as a wave
- Acts as a particle
Photoelectric Effect: Demonstrates light's particle nature (described by Einstein)

Setup:
- Metal has electrons bound by attraction to positive charges in the nucleus
- Light with the right frequency can knock electrons loose, creating an electron current
Photon Interaction:
- Photon (massless particle of light) hits an electron
- If photon has enough energy, it can free the electron
- Freed electron is called a photoelectron
- Energy Conservation:
  - Energy of photon = Energy to free electron (work function) + Kinetic Energy of photoelectron

Energy of Photon:
- Formula: ( E_{photon} = h \cdot \nu )
- Relate frequency to wavelength: ( c = \lambda \cdot \nu )
- Substitute frequency: ( \nu = \frac{c}{\lambda} )
- Energy equation becomes: ( E_{photon} = \frac{h \cdot c}{\lambda} )
Example Calculation:
- Given: Wavelength = 525 nm, Work Function for cesium
- Calculate photon energy using Planck's constant and speed of light
- Photon Energy Result: 3.78 x 10^-19 J
- Compare photon energy with work function to determine if photoelectron is produced
Kinetic Energy and Velocity of Photoelectron:
- Kinetic Energy (KE) formula: ( KE = E_{photon} - \text{work function} )
- Example: KE = 3.5 x 10^-20 J
- Using ( KE = \frac{1}{2}mv^2 ), solve for electron velocity
- Velocity Result: 2.8 x 10^5 m/s

Example of changing wavelength to 625 nm
- Photon Energy: 3.2 x 10^-19 J (lower than work function)
- Lower energy means no photoelectron is produced
- Intensity increase doesn't affect photoelectron production if photon energy is insufficient

The Photoelectric effect is better explained by the particle model of light
Key Takeaway: A photon must have sufficient energy (higher than work function) to produce a photoelectron