Dual Nature of Radiation and Matter - Lecture 4

Introduction

• Topic: Devison and Germer Experiment
• This is the last lecture on the topic.
• Aim: To clarify doubts and explain the concepts in detail.

D. Broglie Hypothesis

• Key Concept: Every moving particle exhibits wave properties.

• Concept of Matter Waves: A moving particle is associated with a wave whose wavelength is defined by:

  [ \lambda = \frac{h}{p} \quad (p = m \cdot v) ]

• This wave property is significant for small particles (e.g., electrons) and negligible for large objects.

Need for the Experiment

• To prove the wave nature of electrons.
• Previous theories of D. Broglie needed experimental verification.

Devison and Germer Experiment

• Conducted to demonstrate diffraction of electrons, confirming their wave-like behavior.
• Key Findings: Fast moving electrons show diffraction, which is a property of waves.
• This proved that electrons can behave as waves.

Similar Experiment by G.P. Thomson

• Conducted a similar experiment confirming electron diffraction.
• Both Devison and Germer, and G.P. Thomson were awarded Nobel Prizes for their work.

Experimental Setup

1. Filament:
   • Made of Tungsten, heated to emit electrons via thermionic emission.
2. Barium Oxide Coating:
   • Provides a low work function for easier electron emission.
3. Fine Cylinder:
   • Helps shape the electron beam through a fine hole.
4. High Voltage:
   • Applied to accelerate the emitted electrons.
5. Nickel Crystal:
   • Used for electron diffraction.
6. Movable Detector:
   • Measures the intensity of scattered electrons at various angles.

Results of the Experiment

• Observed diffraction patterns indicating areas of constructive and destructive interference.
• Intensity peaks were noted at specific angles (e.g., 50 degrees) for varying voltages (e.g., 54 volts).
• This matching of intensity with angle demonstrated the wave properties of electrons.

Bragg's Law

• Important for understanding crystal diffraction:

  [ 2d \sin(\theta) = n\lambda ]

• Where:

  • (d): Distance between atomic layers
  • (\theta): Angle between incident wave and atomic layer
  • (n): Order of maxima (integer)

Experimental Observations

• When electrons strike the Nickel crystal, diffraction occurs, showing wave properties.
• Even single electrons display wave-like behavior when not observed directly, indicating they are not just particles.

Conclusion

• Results affirm D. Broglie's hypotheses on wave-particle duality.
• The experiment provides insight into the nature of matter at quantum levels, supporting the idea that particles like electrons can exhibit wave properties under certain conditions.

Final Notes

• This experiment is pivotal in establishing the dual nature of matter, influencing quantum mechanics profoundly.
• Review key formulas: (\lambda = \frac{h}{p}) and Bragg's Law for deeper understanding.

Remember: The significance of the Devison and Germer experiment cannot be overstated as it validated the wave nature of matter.

Stay tuned for more detailed understanding in future lectures!