The Davisson-Germer Experiment is a key experiment that confirms the wave nature of particles, specifically electrons, as predicted by de Broglie. This experiment demonstrates that particles like electrons can exhibit diffraction, a property of waves, which supports the existence of de Broglie waves.
What is de Broglie’s Hypothesis?
In 1924, Louis de Broglie proposed that all matter has wave-like properties. He suggested that the wavelength (λ) of a particle is related to its momentum (p) by the formula:
Where:
- = wavelength of the particle
- = Planck’s constant ()
- = momentum of the particle (, where is mass and is velocity)
This idea led to the concept of matter waves (also called de Broglie waves).
Davisson-Germer Experiment Overview
The Davisson-Germer experiment was conducted in 1927 by Clinton Davisson and Lester Germer. It aimed to study how electrons scatter off a crystal surface. The unexpected result was the discovery of electron diffraction, proving that electrons have wave-like behavior, just as light does.
Setup of the Experiment
- Electron gun: This emits a beam of electrons.
- Nickel target: A nickel crystal acts as a diffraction grating.
- Electron detector: Measures the intensity of scattered electrons at different angles.
- Accelerating voltage: Controls the speed (and thus the momentum) of the electrons.
How the Experiment Works
Electron emission: Electrons are emitted from an electron gun and accelerated by a potential difference (V). The kinetic energy of the electrons is given by:
Where:
- is the kinetic energy of the electrons
- is the charge of the electron ()
- is the accelerating voltage
Momentum of electrons: The momentum of an electron is related to its kinetic energy:
Where:
- is the mass of the electron ()
- is the accelerating voltage
Electron diffraction: When the electron beam strikes the nickel crystal, the atoms of the crystal scatter the electrons. The crystal structure acts like a diffraction grating for the electron waves.
Measurement of angles: The scattered electrons are detected at various angles, and the intensity of the scattered electrons is measured. A sharp peak in intensity occurs at specific angles, showing constructive interference, a key sign of wave behavior.
Bragg’s Law
The observed diffraction pattern can be explained by Bragg’s law, which relates the angle of diffraction () to the wavelength of the electrons and the spacing between the crystal planes (d):
Where:
- = order of the diffraction (usually for the first-order diffraction)
- = spacing between crystal planes
- = angle of incidence that results in constructive interference
- = wavelength of the electron (from de Broglie’s equation)
Verifying de Broglie’s Hypothesis
Using the de Broglie wavelength for the electrons:
By adjusting the accelerating voltage (V), the wavelength of the electrons can be changed. The diffraction pattern observed at different angles confirms that the electrons behave like waves, with their wavelength matching de Broglie’s prediction.
Results of the Experiment
At a specific accelerating voltage (around 54V), a sharp diffraction peak was observed at an angle of about 50°. Using Bragg’s law, the electron wavelength was calculated and found to match the de Broglie wavelength, confirming the wave nature of electrons.
Key Takeaways for Students:
- Wave-particle duality: The Davisson-Germer experiment confirms that particles such as electrons can behave as waves, supporting de Broglie’s hypothesis.
- Diffraction pattern: The diffraction of electrons off the nickel crystal proves that particles can undergo constructive and destructive interference, a wave-like property.
- De Broglie wavelength: The experiment provides experimental evidence for the de Broglie wavelength of matter waves.
This experiment is crucial because it supports quantum mechanics' view that matter, on a small scale, behaves as both particles and waves.
