Davisson and Germer Experiment

 

 

The Davisson and Germer experiment was a 1923-27 experiment performed by Clinton Davisson and Lester Germer to establish the wave nature of slow moving electrons. This confirmed the de-Broglie hypothesis of wave-particle duality.

Experimental setup of Davisson and Germer Experiment

The Davisson and Germer experiment is contained in a vacuum chamber so that electron deflection and scattering by the medium are avoided. The major components of the experimental setup are following:

Electron gun: An electron gun is a Tungsten filament(F) coated with barium oxide(barium oxide and other alkali oxides helps in decreasing the work function of the tungsten cathode. Work function of uncoated tungsten is 4.5 eV  and of coated tungsten is 1.5 eV. Thus the cathode can emit electrons at a relatively low temperature which is highly economical) that produces electrons by thermionic emission.

Electrostatic particle accelerator: To accelerate electrons at a known potential, two oppositely charged plates (positive and negative plate) are employed.

Collimator: The accelerator is housed within a cylinder C with a restricted path for electrons running along its axis. Its purpose is to prepare a narrow and straight beam of electrons.

Target: N is a nickel crystal cut along cubical diagonal. The nickel crystal is positioned in such a way that it may be rotated around a fixed axis.

Detector: D is an electron detector which is used to collect dispersed electrons from the Ni crystal. It is connected to a sensitive galvanometer. As illustrated in the picture below, the detector may be rotated on a semicircular arc.

 

Working of Davisson and Germer Experiment

•  A fine beam of accelerated electrons obtained from the electron gun is made to fall normally on the surface of Ni crystal.
• The experiment was performed by varying the accelerating voltage from 44 V to 68 V.
• These accelerated electrons are scattered in different directions by the atoms of the Ni crystal.
• The intensity (I) of the scattered electron beam is recorded by the electron detector D by moving it on circular scale at different values of scattering angle ϕ (angle between the incident and scattered electron beams).

Observation of Davisson and Germer Experiment

• The intensity (I) of the electronic current received by the detector, as well as the scattering angle ϕ, were investigated for different accelerating voltage.
• The accelerated electrons intensity was not constant. It displayed a maximum and a lowest value.
• It was noticed that at an accelerating voltage of 54 V and at scattering angle ϕ = 50^º the intensity I was maximum.
• The appearance of peak in intensity in a particular direction is due to constructive interference of scattered electrons from different layers of regularly spaced atoms of the Ni crystal, i.e., the differentiation of electrons takes place.

Davisson and Germer Experiment Results

 

In the above figure θ is called the glancing angle and ϕ is scattering angle. For ϕ = 50^º :-

θ + ϕ + θ = 180^º

Or

θ = (180^º – ϕ)/2 = 65^º

From X-ray scattering, the value of lattice spacing is d = 0.91 Å.

According to Bragg’s law, for first order diffraction maxima (n = 1), we get

2 d sinθ = 1 × λ

⇒ 2 × 0.91 sin 65^º = 1 × λ

⇒ λ = 1.65 Å

According to de-Broglie’s wave-particle duality, the wavelength of the wave associated with electron is given by

⇒ λ = 1.66 Å

As a result, the experimental results correspond well with the theoretical values obtained from the de Broglie equation.

This proves the existence of the de-Broglie waves for the slow moving electrons.

 

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