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# Davisson-Germer Experiment

The Davisson and Germer Experiment established the wave nature of electrons and validated the de Broglie equation for the first time. De Broglie proposed the dual nature of the matter in 1924, but it wasn’t until later that Davisson and Germer’s experiment confirmed the findings. The findings provided the first experimental verification of quantum mechanics. We shall investigate the scattering of electrons by a Ni crystal in this experiment. Let us investigate more.

### Construction of Davisson Germer Experiment

The Davisson and Germer experiment is contained within a vacuum chamber. As a result, electron deflection and scattering by the medium are avoided. The following are the major components of the experimental setup:

Electron gun: An electron gun is a Tungsten filament that produces electrons by thermionic emission, which means that it emits electrons when heated to a specific temperature.

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 with a restricted path for electrons running along its axis. Its purpose is to prepare a narrow and straight (collimated) electron beam for acceleration.

Target: The goal is to find a nickel crystal. On the Nickel crystal, the electron beam is fired normally. The crystal is positioned in such a way that it may be rotated around a fixed axis.

Detector: A detector is used to collect dispersed electrons from the Ni crystal. As illustrated in the picture below, the detector may be moved in a semicircular arc. ### Working of Davisson Germer experiment

• A low voltage power supply was used to heat an electron cannon with a tungsten filament F coated with barium oxide.
• When an appropriate potential difference is applied from a high voltage power source, the electron cannon produces electrons that are then accelerated to a certain velocity.
• These released electrons were forced to travel through a cylinder perforated with small holes along its axis, resulting in a finely collimated beam.
• The cylinder’s beam is once more directed toward the surface of a nickel crystal. As a result, electrons disperse in numerous ways.
• The intensity of the electron beam created is recorded by the electron detector, and it is then moved on a circular scale after being linked to a sensitive galvanometer (to record the current).
• The intensity of the scattered electron beam is measured for different values of angle of scattering by moving the detector on the circular scale at different places that change the θ (angle between the incident and scattered electron beams).

### Observations of Davisson Germer experiment

We may draw the following conclusions from this experiment:

• Only the existence of an electron in the form of a particle may be detected by the detector utilised here. As a consequence, the detector receives electrons as an electronic current.
• The intensity (strength) of the electronic current received by the detector, as well as the scattering angle, are being investigated. This current is referred to as the electron intensity.
• The dispersed electrons intensity is not constant. It displays a maximum and the lowest value that correspond to the maxima and minima of an X-ray diffraction pattern.
• By varying the angle of scattering (θ), we were able to get a change in the intensity (I) of the scattered electrons.
• The accelerated voltage was adjusted from 44V to 68V by varying the accelerating potential difference. We could detect a significant peak in the intensity (I) of the scattered electron with an accelerating voltage of 54 V at a scattering angle of 50°.
• This peak was caused by the constructive interference of electrons dispersed from various layers of the crystal’s evenly spaced atoms. The wavelength of matter waves was determined using electron diffraction to be 0.165 nm.

### The Idea Behind the Experiment Setup

The Davisson and Germer experiment was based on the assumption that waves reflected from two distinct atomic levels of a Ni crystal will have a fixed phase difference. Following reflection, these waves will either interact constructively or destructively. As a result, a diffraction pattern is produced.

Waves were employed in place of electrons in the Davisson and Germer experiment. These electrons drew together to produce a diffraction pattern. Thus, the dual nature of substance was established. The de Broglie equation and Bragg’s law can be related as illustrated below:

According to the de Broglie equation, we have:

λ = h ⁄ p

= h ⁄ √(2m E)

= h ⁄ √(2m eV)

where,

• m is the mass of an electron,
• e is the charge on an electron, and
• h is the Plank’s constant.

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

Bragg’s Law is given by the following equation:

nλ = 2d sin(90° − θ ⁄ 2)

Since the value of d from the X-ray diffraction investigations was previously known, we can get the wavelength of the waves creating a diffraction pattern from the equation for a variety of values of θ.

### Davisson and Germer Experiment Results

The Davisson and Germer experiment yields a value for the scattering angle and a matching value of the potential difference V at which electron scattering is greatest. Thus, when these two values from Davisson and Germer’s data are applied in both equations, they produce identical results for λ. As a result, de Broglie’s wave-particle duality is established, and his equation is verified, as illustrated below:

λ = h ⁄ √(2m eV)

For V = 54 V,

λ = 12.27/√(54) nm

= 0.167 nm

The value of ‘d’ obtained from X-ray scattering is now 0.092 nm. As a result, with V = 54 V, the angle of scattering is 50°, and we can use this in the equation to get:

n λ = 2 (0.092 nm) sin( 90° − 50°/2)

For n = 1, we have:

λ = 0.165 nm

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

### Sample Questions

Question 1: What was the objective of the classic Davisson-Germer experiment with electrons?

The Davisson-Germer experiment was carried out to confirm the wave character of electrons. It is the first experiment that provides evidence for the wave nature of matter.

Question 2: An electron beam with an energy of 75 eV falls naturally on the surface through the crystal in the Davisson-Germer experiment. What is the interatomic distance in the crystal lattice plane if the maxima of order I obtained at an angle of 45° to the direction incident?

nλ = 2d sinθ

Also, λ = h ⁄ √(2m eV)

So, for n =1:

h ⁄ √(2m eV) = 2d sin45°

12.27 ⁄ √75 = 2d × 1 ⁄ √2

1.41 = 1.41d

d = 1 A°

Hence, the interatomic distance in the plane is 1 A°.

Question 3: In the Davisson – Germer experiment, which crystal is used?

Nickel crystal was employed in the Davisson – Germer experiment. The surface of the nickel crystal is bombarded with a narrow stream of electrons. As a result, the electrons are scattered in all directions by the crystal’s atoms.

Question 4: Which of the following theories is supported by the Davisson-Germer experiment?

The Davisson and Germer experiment demonstrates the wave nature of matter particles. The Davisson–Germer experiment gives crucial evidence of the de-Broglie hypothesis, which states that particles such as electrons have a dual nature.

Question 5: If a stationary proton and a particle are propelled by the same potential difference, what will be the de-Broglie wavelength ratio?

The gain in K.E. of a charge particle after passing through a potential difference of V is expressed as eV, which is also equal to (1⁄2mv2) where v is the charge particle’s velocity.

1 ⁄ 2 m v2 = q V

v = √(2 q V ⁄ m)

​⇒ m v =  √(2 m q V)

de-Broglie wavelength,

λ = h ⁄ m v = h ⁄ √(2 m q V)

λp ⁄ λα = √(mα qα Vα ⁄ mp qp Vp)

λp ⁄ λα = √((4 × 2) ⁄ (1 × 1)) = 2√2

Hence, the de-Broglie wavelength ratio is equal to 2√2.

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