Davisson and Germer Experiment

The Davisson and Germer Experiment was the first to prove that electrons are waves and to validate the de Broglie equation. In 1924, De Broglie hypothesized the dual nature of matter, but Davisson and Germer’s experiment did not validate the conclusions until much later. The findings proved quantum mechanics for the first time in an experimental setting. In this experiment, we will explore electron scattering by a Ni crystal.

CONSTRUCTION:

The construction of the Davisson and Germer experiment includes a vacuum chamber in which the medium has no effect on electron deflection or scattering. The main elements of the experimental setup are as follows:

Electron Gun:

It is a Tungsten filament which produces electrons via thermionic emission, which means it emits electrons when heated to a specified temperature.

Electrostatic Particle Accelerator:

Two oppositely charged plates (+ve and -ve plate) are used to accelerate electrons at a known potential.

Collimator: 

The accelerator is contained within a cylinder with a narrow channel for electrons flowing along its axis. Its function is to accelerate an electron beam that is narrow and straight (collimated).

Target: 

Finding a nickel crystal is the objective. The electron beam is generally fired on the Nickel crystal. The crystal is set up so that it may be rotated around a fixed axis.

Detector: 

To collect the dispersed electrons from the Ni crystal, a detector is employed. The detector is moved in a semicircular arc.

DAVISSON GERMER’S EXPERIMENT IS IN THE PROCESS OF BEING CARRIED OUT:

• An electron cannon with a tungsten filament F coated in barium oxide was heated using a low voltage power supply.
• The electron cannon creates electrons that are subsequently accelerated to a specific velocity when a specific potential difference is provided from a high voltage power source.
• The liberated electrons were forced to go through a cylinder with microscopic holes perforated along its axis, resulting in a finely collimated beam.
• The cylinder’s beam is aimed at the surface of a nickel crystal once more. As a result, electrons spread in a variety of directions.
• The electron detector records the intensity of the generated electron beam, which is then moved on a circular scale after being connected to a sensitive galvanometer (to record the current).
• The intensity of the scattered electron beam is measured at various angles of scattering by moving the detector around the circular scale at various locations that modify the (angle between the incident and scattered electron beams).

OBSERVATIONS:

The following are some of the conclusions we may derive from this experiment:

• The detector used here can only detect the presence of an electron in the form of a particle. As a result, electrons are received as an electric current by the detector.
• The intensity (strength) of the electrical current received by the detector is being examined, as well as the scattering angle. The electron intensity is the name given to this current.
• The intensity of distributed electrons varies. It shows the highest and lowest values, which correspond to the peaks and valleys of an X-ray diffraction pattern.
• We were able to modify the intensity (I) of the dispersed electrons by changing the scattering angle theta.
• By adjusting the accelerating potential difference, the accelerated voltage was varied from 44 to 68 volts. With an accelerating voltage of 54 V and a scattering angle of 50°, we were able to identify a large peak in the intensity (I) of the scattered electron.
• The constructive interference of electrons scattered from several layers of the crystal’s equally spaced atoms created this peak. The wavelength of matter waves was determined to be 0.165 nm via electron diffraction.

THE EXPERIMENT SETUP’S INSPIRATION:

The Davisson and Germer experiment assumed that waves reflected from two different atomic layers of a Ni crystal will have a fixed phase difference. These waves will interact constructively or destructively after they have reflected. A diffraction pattern emerges as a result of this process.

In Davisson and Germer’s experiment, waves were used instead of electrons. A diffraction pattern was created when the electrons pulled together. As a result, the dual nature of matter has been established. The following diagram shows how the de Broglie equation and Bragg’s law are linked:

We have the following de Broglie equation:

λ = h/p

   = h/ √(2mE)

   = h/ √ (2m eV)

Where, m = mass of an electron

               e = charge on an electron

               h = Plank’s constant.

As a result, an electron has a wavelength determined by the equation for a given V.

The following equation expresses Bragg’s Law:

nλ = 2d sin (90° − θ ⁄ 2)

The wavelength of the waves that create a diffraction pattern can be derived from the equation for a variety of values because the value of d from the X-ray diffraction research was previously known.

RESULTS OF THE DAVISSON AND GERMER EXPERIMENT:

The Davisson and Germer experiment give a scattering angle and a corresponding potential difference V at which electron scattering is maximum. As a result, applying these two values from Davisson and Germer’s data to both equations yields identical results for. De Broglie’s wave-particle duality is demonstrated as a result, and his equation is verified, as seen below:

λ = h/ √(2mE)

V = 54V

λ = 12.27/ √ (54) nm

    = 0.167 nm

Using X-ray scattering, the value of ‘d’ has now been determined to be 0.092 nm. As a result, the angle of scattering is 50° when V = 54 V, and we can utilize this in the equation to get:

nλ = 2(0.092 nm) sin (90 ̊ – 50 ̊/2) 

for n = 1, λ = 0.165 nm

The result of the experiment matches the theoretical values derived from the de Broglie equation quite well.

CONCLUSION:

Electrons are dispersed off a crystalline nickel surface in the Davisson–Germer experiment. Electron matter wave diffraction patterns are noticed. They provide proof of the existence of matter waves. Diffraction investigations with various particles reveal matter waves. When electron beams are conducted through atomic crystals, diffraction occurs, as demonstrated by the Davisson and Germer experiment. This demonstrates that electrons’ wave nature can cause interference and diffraction.