Wave-Particle Duality (Copy)

• Dual Nature of Light and Matter

• Light shows both wave and particle characteristics.
  • Wave nature: shown through interference and diffraction.
  • Particle nature: shown through photoelectric effect.
• Matter also shows wave-like properties, especially electrons, when passed through narrow slits (e.g. electron diffraction).

• Electron Diffraction Evidence

• Electrons passed through thin graphite foil produce interference rings.
• This behavior confirms that electrons behave as waves.
• The rings form due to diffraction, which requires a wavelength, implying that electrons possess a de Broglie wavelength.

• The de Broglie Hypothesis

• Proposed by Louis de Broglie: all matter particles (like electrons) have a wavelength associated with their momentum.
• The de Broglie equation:

  λ = h / p

  where:
  λ = de Broglie wavelength (in meters)
  h = Planck’s constant = 6.63 × 10⁻³⁴ J·s
  p = momentum = mv

• If the particle’s kinetic energy is given, use:

  λ = h / √(2 m E)

  where:
  m = mass of particle
  E = kinetic energy of the particle

• Wave-Particle Duality Summary

• Conditions to Observe Wave Nature of Matter

• Wave behavior is observable only when the object is extremely small (e.g. electrons, neutrons).
• The de Broglie wavelength must be comparable to slit size or object features.
• For macroscopic objects (e.g. a car), the de Broglie wavelength is negligible (around 10⁻³⁵ m).

• de Broglie Wavelength Applications

• Used in:
  • Electron microscopes
  • Diffraction experiments
  • Quantum mechanics predictions

• Relation to Uncertainty Principle

• Heisenberg’s uncertainty principle:
  Δx Δp ≥ h / (4π)

  This implies the more precisely you know momentum (p), the less precisely you can know position (x), and vice versa.

• Important Formulae to Memorise

1. λ = h / p
2. p = mv
3. λ = h / √(2 m E)
4. E = hf
5. p = E / c

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course