Overview
This lecture introduces the ultraviolet catastrophe, Planck’s solution with quantized energy, Einstein’s photoelectric effect experiments, and the dual nature of light as both a wave and a particle. It emphasizes key formulas and concepts essential to quantum physics.
Ultraviolet Catastrophe
- Heating objects causes them to emit higher frequency radiation as temperature increases.
- Classical physics predicted unlimited UV radiation from hot objects, which contradicted real-world observations.
- Life exists, so the universe is not flooded with ultraviolet radiation as classical models suggested.
- Actual emission data showed a curve rather than a linear increase with temperature.
Planck’s Solution
- Max Planck assumed energy is quantized, existing only in minimum discrete units.
- Planck fit the experimental curve by introducing a constant (Planck's constant).
- Derived the relationship: energy of light (E) = Planck’s constant (h) × frequency (f).
- Planck’s constant: h = 6.626 × 10⁻³⁴ Joule·seconds.
Einstein and the Photoelectric Effect
- The photoelectric effect: shining light on metal only ejects electrons above a certain frequency threshold.
- Increasing light intensity at low frequency does not eject electrons.
- Electrons are ejected instantly at high frequency, regardless of intensity.
- Proved light behaves as particles (photons), not just waves.
Particle Theory of Light & Photons
- A photon is a particle of light; its energy is called a quantum.
- The energy of a photon: E = h × f.
- For multiple photons: E_total = n × h × f, where n = number of photons.
- Light exhibits both wave and particle properties (wave-particle duality).
Key Terms & Definitions
- Ultraviolet Catastrophe — Predicted infinite UV radiation from heated objects, which did not occur in reality.
- Quantized Energy — Energy that exists in discrete, indivisible units.
- Planck’s Constant (h) — The proportionality constant in E = h × f; 6.626 × 10⁻³⁴ J·s.
- Photoelectric Effect — Ejection of electrons from a metal when exposed to light above a threshold frequency.
- Photon — A quantized particle of light.
- Quantum — The minimum possible unit of energy.
Action Items / Next Steps
- Memorize Planck’s constant: h = 6.626 × 10⁻³⁴ Joule·seconds.
- Review and memorize the formula: E = h × f.
- Prepare for example problems applying Planck’s equation in the next session.