Davisson Germer experiment (Electron Diffraction)

Davisson-Germer Experiment (Electron Diffraction)

The Davisson-Germer experiment demonstrated the wave nature of electrons through the phenomenon of electron diffraction. It provided experimental confirmation of de Broglie’s hypothesis that particles like electrons exhibit wave-like behavior. This experiment was a pivotal moment in quantum mechanics and contributed significantly to the concept of wave-particle duality.

Objective:

To study the diffraction of electrons by a crystalline solid and to verify the wave nature of matter, supporting de Broglie’s hypothesis.

Experimental Setup:

The experimental apparatus consists of:

• Electron Gun: Emits a beam of electrons, accelerated by a high voltage.
• Nickel Crystal Target: Used as the diffracting medium due to its regular atomic arrangement, acting as a diffraction grating.
• Detector (Faraday Cup): Collects electrons after diffraction and measures their intensity.
• Rotatable Detector Arm: Allows measurement of electron intensity at different angles, important for analyzing electron diffraction patterns.
• High Voltage Power Supply: Accelerates the electrons.

Procedure:

1. Electrons are emitted from the electron gun and accelerated by a voltage (V).
2. The accelerated electrons strike a nickel crystal, which acts as a diffraction grating.
3. The diffracted electrons are detected at various angles by the rotatable detector.
4. The intensity of the scattered electrons is measured as a function of the angle of scattering, revealing the electron diffraction pattern.

Observations:

1. A sharp peak in intensity is observed at a specific angle, corresponding to constructive interference. This diffraction pattern is similar to X-ray diffraction, confirming the wave nature of electrons.
2. The diffraction pattern provides insights into the underlying atomic structure, confirming the validity of quantum mechanics.

Key Result:

The observed diffraction angle (θ) and the spacing between atomic planes of the nickel crystal (d) satisfy Bragg’s law:

n λ = 2d sin θ

Where:

• n: Order of diffraction,
• λ: Wavelength of electrons,
• d: Spacing between atomic planes in the crystal,
• θ: Angle of diffraction.

This equation ties the experimental results directly to the wave nature of matter and electron diffraction.

Relation to de Broglie Wavelength:

The wavelength of the electrons is given by de Broglie’s equation:

λ = h / p = h / √(2mₑ eV)

Where:

• h: Planck’s constant (6.63 × 10⁻³⁴ J·s),
• p: Momentum of the electron,
• mₑ: Mass of the electron (9.1 × 10⁻³¹ kg),
• e: Charge of the electron (1.6 × 10⁻¹⁹ C),
• V: Accelerating voltage (V).

This equation links the experiment’s results to the wavelength of matter waves and reinforces de Broglie’s hypothesis about the wave nature of electrons.

Significance:

1. The experiment confirmed the wave nature of electrons, as proposed by de Broglie, providing direct evidence of matter waves.
2. It provided a direct measurement of the wavelength of electrons, highlighting the application of quantum mechanics.
3. It established the validity of wave-particle duality, a key principle in quantum mechanics, shaping modern physics.

Applications:

• Electron Microscopy: Uses the wave nature of electrons to achieve high-resolution imaging, leveraging electron diffraction for precise analysis.
• Crystallography: Electron diffraction techniques are used to study atomic structures and explore the arrangement of atoms in materials.
• Quantum Mechanics: Reinforces the principles of quantum theory and wave-particle duality, demonstrating that matter exhibits both particle-like and wave-like behavior.

The Davisson-Germer experiment was a groundbreaking achievement in physics, confirming that matter exhibits both particle-like and wave-like behavior. It played a pivotal role in the development of quantum mechanics and modern technology, further validating the de Broglie hypothesis and the concept of wave-particle duality.