Wave-Particle Duality Demonstration

Introduction

• Topic: Wave-particle duality of electrons.
• Context: Second year quantum mechanics class.
• Objective: Provide experimental proof that electrons can behave like waves.

Challenges in Demonstration

• Young's Double Slit Experiment: Difficult to perform with electrons.
• Optics: Complex but important for applications like electron microscopes.
• Diffraction: An easier method to demonstrate wave behavior of electrons.

Diffraction and Bragg's Law

• Bragg Diffraction: X-rays reflect off crystal planes causing interference patterns.
• Electron Diffraction: Similar to X-rays, electrons should behave like waves and produce interference patterns when diffracted.

Experimental Setup

• Apparatus: Similar to a CRT (Cathode Ray Tube) in old televisions.
• Components:
  • Filament: Heats up to emit electrons.
  • Positively charged plate: Attracts electrons through a slit.
  • Target: Mesh coated with graphite powder.
• Graphite Structure:
  • Consists of stacked sheets of carbon atoms.
  • Sheets provide planes for electron diffraction.

Detailed Equipment Description

• Electron Gun:
  • Emits electrons when filament heats up.
  • Electrons attracted towards positively charged plate.
  • Electrons accelerate and pass through a slit.
• Graphite Target:
  • Acts as a diffraction grating.
  • Electrons undergo diffraction when passing through.

Phosphor Screen

• Electrons hitting the screen emit light.
• Similar to old television screens with phosphor materials.

Experiment Observations

• Particle Behavior: Electrons scatter randomly if behaving like particles.
• Wave Behavior: Electrons create interference patterns if behaving like waves.
  • Constructive interference leads to bright spots.
  • Destructive interference leads to dark spots.

De Broglie Relation

• Links momentum and wavelength: Higher momentum, shorter wavelength.
• Experiment aims to show diffraction when electron wavelength matches plane spacing in graphite.

Procedure

1. Supply power to the filament.
2. Apply voltage to accelerate electrons.
3. Increase voltage to match electron wavelength with graphite planes.
4. Observe diffraction pattern on phosphor screen.

Conclusion

• Successful demonstration of wave-particle duality by observing rings indicating wave behavior of electrons.