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# Davisson and Germer Experiment

Davisson and Germer Experiment, for the first time, proved the wave nature of electrons and verified the de Broglie equation. de Broglie argued the dual nature of matter back in 1924, but it was only later that Davisson and Germer experiment verified the results. The results established the first experimental proof of quantum mechanics. In this experiment, we will study the scattering of electrons by a Ni crystal. Let’s find out more.

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## Davisson and Germer Experiment

(Source: Wikipedia)

The experimental setup for the Davisson and Germer experiment is enclosed within a vacuum chamber. Thus the deflection and scattering of electrons by the medium are prevented. The main parts of the experimental setup are as follows:

• Electron gun: An electron gun is a Tungsten filament that emits electrons via thermionic emission i.e. it emits electrons when heated to a particular temperature.
• Electrostatic particle accelerator: Two opposite charged plates (positive and negative plate) are used to accelerate the electrons at a known potential.
• Collimator: The accelerator is enclosed within a cylinder that has a narrow passage for the electrons along its axis. Its function is to render a narrow and straight (collimated) beam of electrons ready for acceleration.
• Target: The target is a Nickel crystal. The electron beam is fired normally on the Nickel crystal. The crystal is placed such that it can be rotated about a fixed axis.
• Detector: A detector is used to capture the scattered electrons from the Ni crystal. The detector can be moved in a semicircular arc as shown in the diagram above.

### The Thought Behind the Experimental Setup

The basic thought behind the Davisson and Germer experiment was that the waves reflected from two different atomic layers of a Ni crystal will have a fixed phase difference. After reflection, these waves will interfere either constructively or destructively. Hence producing a diffraction pattern.

In the Davisson and Germer experiment waves were used in place of electrons. These electrons formed a diffraction pattern. The dual nature of matter was thus verified. We can relate the de Broglie equation and the Bragg’s law as shown below:

From the de Broglie equation, we have:

λ = h/p

= h/$$\sqrt[]{2mE}$$

= h/$$\sqrt[]{2meV}$$     … (1)

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

Therefore for a given V, an electron will have a wavelength given by equation (1).

The following equation gives Bragg’s Law:

nλ = 2d sin($$90^{0}$$-θ/2)     …(2)

Since the value of d was already known from the X-ray diffraction experiments. Hence for various values of θ, we can find the wavelength of the waves producing a diffraction pattern from equation (2).

### Observations of the Davisson and Germer Experiment

The detector used here can only detect the presence of an electron in the form of a particle. As a result, the detector receives the electrons in the form of an electronic current. The intensity (strength) of this electronic current received by the detector and the scattering angle is studied. We call this current as the electron intensity.

The intensity of the scattered electrons is not continuous. It shows a maximum and a minimum value corresponding to the maxima and the minima of a diffraction pattern produced by X-rays. It is studied from various angles of scattering and potential difference. For a particular voltage (54V, say) the maximum scattering happens at a fixed angle only ( $$50^{0}$$ ) as shown below:

Plots between I – the intensity of scattering (X-axis) and the angle of scattering θ for given values of Potential difference.

### Results of the Davisson and Germer Experiment

From the Davisson and Germer experiment, we get a value for the scattering angle θ and a corresponding value of the potential difference V at which the scattering of electrons is maximum. Thus these two values from the data collected by Davisson and Germer, when used in equation (1) and (2) give the same values for λ. Therefore, this establishes the de Broglie’s wave-particle duality and verifies his equation as shown below:

From (1), we have:

λ = h/$$\sqrt[]{2meV}$$

For V = 54 V, we have

λ = 12.27/$$\sqrt[]{54}$$ = 0.167 nm  …. (3)

Now the value of ‘d’ from X-ray scattering is 0.092 nm. Therefore for V = 54 V, the angle of scattering is $$50^{0}$$, using this in equation (2), we have:

nλ = 2 (0.092 nm)sin( $$90^{0}-50^{0}/2)$$

For n = 1, we have:

λ = 0.165 nm ….. (4)

Therefore the experimental results are in a close agreement with the theoretical values got from the de Broglie equation. The equations (3) and (4) verify the de Broglie equation.

Can  a small particle be at multiple places at the same time? Learn more about Wave Nature of Matter here.

## Solved Example for You

Q. Statement-1: Davisson- Germer experiment established the wave nature of electrons.
Statement-2: If electrons have wave nature, they can interfere and show diffraction.

1. Statement -1 is false, statement -2  is true.
2. Both the statements are false.
3. Statement – 1 is true, statement – 2 is true, Statement – 2 is correct explaination of Statement – 1
4. Statement – 1 is true, statement – 2 is true, Statement – 2 is not the correct explaination of Statement – 1.

Solution: C. The Davisson and Germer experiment showed that electron beams can undergo diffraction when passed through the atomic crystals. This shows that the wave nature of electrons as waves can exhibit interference and diffraction.

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