Davisson–Germer Experiment
Direct experimental proof of the wave nature of electrons – electron diffraction by a nickel crystal
The Problem: Particle vs Wave Nature of Electrons
Early atomic models treated electrons solely as particles. However, de Broglie’s hypothesis (1924) proposed that particles like electrons have an associated wavelength: λ = h / p (where h is Planck’s constant, p is momentum). In 1927, Clinton Davisson and Lester Germer performed a landmark experiment that demonstrated electron diffraction, confirming de Broglie’s wave-particle duality. They shared the Nobel Prize in 1937.
The experiment involved firing a beam of electrons at a crystalline nickel target and observing the angular distribution of scattered electrons. The observed diffraction pattern was analogous to X‑ray diffraction, proving that electrons exhibit wave‑like behavior.
Experimental Setup & Interactive Simulation
The apparatus consists of an electron gun (tungsten filament coated with barium oxide), a collimator, a nickel crystal target, and a movable electron detector (Faraday cup) connected to a galvanometer. The electron beam is accelerated by a variable voltage V, and the detector measures the intensity of scattered electrons as a function of the angle θ relative to the incident beam.
The diagram shows the electron gun, nickel crystal, and movable detector. Adjust voltage and angle. The diffraction maximum occurs near V=54 V and θ=50°, where the de Broglie wavelength matches Bragg’s condition.
According to Bragg’s law for electron diffraction: nλ = 2d sin φ, where φ = (180° – θ)/2 is the angle between the incident beam and the crystal planes. For the nickel (111) planes, d = 0.91 Å.
Experimental Observations: Intensity vs Angle
Davisson and Germer measured the intensity of scattered electrons at various angles for a fixed accelerating voltage. They found a strong maximum at θ = 50° when the voltage was about 54 V. This peak corresponds to first-order diffraction (n=1). The graph below simulates the intensity pattern as you change voltage.
Setup Details
- Electron gun: Tungsten filament coated with barium oxide, heated to emit electrons by thermionic emission.
- Accelerating voltage: Applied between filament and anode, giving electrons kinetic energy E = e·V.
- Collimator: A cylinder with fine holes produces a narrow, collimated electron beam.
- Nickel crystal: Single crystal with known lattice spacing d = 0.91 Å for the (111) plane.
- Detector: Faraday cup connected to a sensitive galvanometer, movable on a circular scale.
Key Observations & Conclusion
- Diffraction maximum observed at V = 54 V, θ = 50°.
- No such maximum would exist if electrons behaved only as classical particles.
- The pattern is identical to X‑ray diffraction from the same crystal.
- Direct verification of de Broglie relation λ = h / p.
- Electrons exhibit both particle and wave nature – foundation of quantum mechanics.
Mathematical Derivation of the Wavelength
The kinetic energy of electrons accelerated through a voltage V is E_k = e·V. Momentum p = sqrt(2 m E_k) = sqrt(2 m e V). Hence de Broglie wavelength:
Using Bragg’s law for first-order diffraction (n=1): λ = 2 d sin φ. In the Davisson–Germer setup, the crystal planes are oriented such that φ = (180° – θ)/2 = 90° – θ/2, so sin φ = cos(θ/2). Therefore:
For nickel, d = 0.91 Å. At the observed peak: V = 54 V, θ = 50°, the calculated λ from electron energy is about 1.67 Å, while Bragg’s condition gives 1.65 Å – remarkable agreement.
Significance of the Davisson–Germer Experiment
- Confirmed de Broglie’s hypothesis of wave-particle duality.
- Provided the first experimental measurement of the de Broglie wavelength for electrons.
- Established electron diffraction as a powerful technique for studying crystal structures (used in electron microscopes and LEED).
- Marked the birth of quantum mechanics as a fully verified theory.
- Led to the development of wave mechanics and the probabilistic interpretation of quantum states.
Video Lecture: Davisson-Germer Experiment in Urdu/Hindi
Detailed explanation of the Davisson-Germer experiment, de Broglie’s hypothesis, Bragg’s law, and electron diffraction in Urdu/Hindi.
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