Lecture 45 — Photon Momentum, Compton Effect, de-Broglie Waves & Heisenberg Uncertainty

Lecturer: Dr. Nurul Izzati Binti Azman
Email: nurulizzati_azman@um.edu.my
Topics Covered:

  • Photon Momentum
  • Compton Effect
  • de-Broglie Waves
  • Heisenberg Uncertainty Principle

Summary

This lecture explores the wave-particle duality that forms the foundation of modern physics. It begins with the particle nature of light through photon momentum, provides experimental proof via the Compton effect, reverses the paradigm with de-Broglie's matter waves, and concludes with the fundamental limits on measurement imposed by Heisenberg's Uncertainty Principle.

01 — Photon Momentum

Key Insight

Even though photons have zero mass, they possess momentum because they carry energy.

Classical vs Modern Physics

  • Classical: $p = mv$ → if $m = 0$, then $p = 0$
  • Modern: Photons have momentum because $E = pc$

Key Equations

Photon energy: $E = hf = \frac{hc}{\lambda}$

Photon momentum: $$p = \frac{h}{\lambda} = \frac{hf}{c} = \frac{E}{c}$$

Why This Matters

  • Light can push objects (solar sails)
  • Explains Compton scattering
  • Foundation of radiation pressure

02 — Compton Effect

Key Insight

The Compton Effect is experimental proof that photons carry momentum.

What Happens

  1. An X-ray photon strikes a loosely-bound electron
  2. The photon transfers momentum to the electron
  3. The electron recoils
  4. The scattered photon has longer wavelength (lower energy)

Key Equation — Compton Shift

$$\Delta \lambda = \lambda' - \lambda = \frac{h}{m_e c}(1 - \cos \theta)$$

Where:

  • $\lambda'$ = scattered wavelength
  • $\lambda$ = incident wavelength
  • $\theta$ = scattering angle
  • $\frac{h}{m_e c} = 2.43 \times 10^{-12}$ m (Compton wavelength of electron)

Why Classical Wave Theory Failed

  • Wave theory could explain scattering
  • Could NOT explain why wavelength increases
  • Only particle collision with momentum conservation explains it

03 — de-Broglie Waves

Key Insight

If light can behave like a particle, can matter behave like a wave?

Answer: YES — every moving particle has a wavelength.

Key Equation — de-Broglie Wavelength

$$\lambda = \frac{h}{p} = \frac{h}{mv}$$

From Kinetic Energy

When velocity is not given directly: $$\lambda = \frac{h}{\sqrt{2m(KE)}}$$

Implications

  • Small particles (electrons, protons): noticeable wave nature
  • Large objects (cars, humans): wavelength too tiny to observe
  • Higher KE → shorter wavelength (fast particles less wave-like)

04 — Heisenberg Uncertainty Principle

Key Insight

Once we accept that particles like electrons are also waves, we cannot pin down their exact location and speed simultaneously.

The Principle

Werner Heisenberg: The more accurately we know position, the less accurately we know momentum, and vice versa.

Key Equation

$$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$$

Where:

  • $\Delta x$ = uncertainty in position
  • $\Delta p$ = uncertainty in momentum

Physical Meaning

  • A wave is spread out — it doesn't have one exact point
  • Therefore, an electron-as-wave cannot have a precise location
  • This is a fundamental limit, not a measurement limitation

Key Takeaways

  1. Wave-Particle Duality: Light and matter both exhibit wave and particle properties
  2. Photon momentum: $p = h/\lambda$ — light can push objects
  3. Compton Effect: Experimental proof of photon momentum
  4. Matter waves: $\lambda = h/p$ — particles have wavelength
  5. Uncertainty Principle: Cannot know position and momentum exactly simultaneously

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