Electromagnetic Radiation and Quantum Theory

Wave or Particle?: The Nature of Light

  • Physicists debated whether light was particles or waves.
  • Evidence suggested light behaved as both particles and electromagnetic waves by 1900.
  • However, the wave theory had limitations.

Ultraviolet Catastrophe

  • Problem: The light-as-wave theory predicted an "ultraviolet catastrophe."
  • Objects emit electromagnetic (EM) radiation due to vibrating electrons.
  • Wave theory predicted that as frequency increases (shorter wavelengths), energy increases steadily.
  • Observed: This holds true for visible light, but diverges in the ultraviolet range.
  • Catastrophe: Very hot objects (stars) would emit all energy instantly if the prediction were true.

Photoelectric Effect

  • Certain metallic materials are photosensitive, emitting electrons (photoelectrons) when interacting with EM radiation.
  • Electrons gain energy (K), but require work (work function, ϕ\phi) to be freed.
  • Wave Theory Prediction: More intensity should eject more electrons with greater energy.
  • Experimental Result: Below a threshold frequency, no electrons are ejected, regardless of intensity.

Planck's Quantum Theory

  • In 1900, Max Planck proposed a new model to solve these problems.
  • EM radiation is not emitted continuously, but in discrete packets of energy (En) called quanta.
  • This suggested light was not a wave, confusing scientists.

Einstein and the Photon

  • In 1905, Albert Einstein showed that quantum energy packets are particle-like photons.
  • Photons are the smallest unit of electromagnetic radiation.
  • EM radiation is composed of photons with specific frequencies and quantized energy.
  • Photon energy is proportional to frequency: E=hvE = hv, where E is energy, v is frequency, and h is Planck’s constant.
  • Planck's constant: h=6.63⋅10−34h = 6.63 \cdot 10^{-34}

Wave-Particle Duality

  • Light is both a particle and a wave depending on the situation.
  • Every particle can also be described as a wave.
  • These small units are often called quanta.

Photon Energy Calculation Example

  • Problem: Find the energy of a photon with a wavelength of 10 nm.
    1. Find the frequency (f): 3×108m/s10nm=f=3×1016Hz\frac{3 × 10^8 m/s}{10 nm} = f = 3 × 10^{16} Hz (note: conversion to meters is implicit in this calculation)
    2. Use Planck's constant to find energy: E=(6.63×10−34)(3×1016Hz)=1.989×10−17JE = (6.63 × 10^{-34})(3 × 10^{16} Hz) = 1.989 × 10^{-17} J
    3. Convert Joules to electron Volts: 1.989×10−17J1.6×10−19J=124eV\frac{1.989 × 10^{-17} J}{1.6 × 10^{-19} J} = 124 eV