Davisson Germer Experiment

Davisson and Germer conducted an experiment that changed how we see particles. They aimed electrons at a nickel crystal and saw the electrons create a wave-like diffraction pattern—something unexpected if electrons were just particles. This proved Louis de Broglie’s idea that particles can also behave like waves. Their discovery was key in developing quantum mechanics and the idea that particles have a dual wave-particle nature. It’s a fundamental concept still taught in physics today.

1.0De-Broglie Wavelength of an Electron

An electron with mass m and charge e, accelerated from rest through a potential difference V, gains kinetic energy equal to the work done by the electric field.

K.E gained by the electron, $K=\frac{1}{2}m{v}^2=\frac{p^2}{2m}$

Work done on the electron =eV

$K=\frac{p^2}{2m}=eV$

$p=\sqrt{2mK}=\sqrt{2meV}$

de Broglie wavelength of the electron is

$\lambda =\frac{h}{p}=\frac{h}{\sqrt{2mK}}=\frac{h}{\sqrt{2meV}}$

Now 

$h=6.63\times 10^{-34}Js,m=h=9.1\times 10^{-31}kg,e=1.6\times 10^{-19}C$

$\therefore \lambda =\frac{6.63\times 10^{-34}}{\sqrt{2\times 9.1\times 10^{-31}\times 1.6\times 10^{-19}V}}\models \frac{12.3\times 10^{-10}}{\sqrt{V}}m=\frac{12.3}{\sqrt{V}}\mathring{A}$

For an accelerating potential of 120 V, the electron’s wavelength is found to be $\lambda =0.112nm$ comparable to the spacing between atomic planes in crystals. This supports the idea that electron matter waves can be observed through diffraction. 

2.0Davisson-Germer Experiment

3.0Construction of Davisson-Germer Experiment

1. Electron Gun: Includes a filament heated by a low tension battery (L.T.B.) which emits electrons through thermionic emission.
2. Anode: A positively charged electrode that accelerates the emitted electrons using a high tension battery (H.T.B.), forming a focused electron beam.
3. Nickel Crystal: Acts as a target, placed at a fixed angle inside a vacuum chamber, which provides a clean environment for the electrons to interact with the crystal lattice.
4. Movable Collector: A detector that rotates around the crystal to measure the intensity of scattered electrons at various angles. It is connected to a galvanometer to record the signal.
5. Vacuum Chamber: Encloses the setup to avoid interference from air molecules and ensure free electron travel.

4.0Working of Davisson-Germer Experiment

1. Electrons emitted from the heated filament are accelerated toward the nickel crystal by a high-voltage battery.
2. The incident electron beam strikes the crystal, and electrons are scattered in various directions due to interaction with the regularly arranged atoms in the crystal.
3. At certain angles, the scattered electron waves interfere constructively, producing intensity maxima that are detected by the movable collector.
4. The intensity of the scattered electrons is recorded at different angles, and a peak intensity is observed at an angle of 50° for an accelerating voltage of 54 V.

 Using Bragg’s Law $n\lambda =2d\sin \theta$ and the known spacing of the nickel crystal, the electron wavelength (λ) was calculated.

This experimental value matched the de Broglie wavelength formula:$\lambda =\frac{h}{\sqrt{2meV}}$ confirming that electrons exhibit wave-like behavior.

The Davisson-Germer experiment gave clear proof of electron diffraction, confirming that electrons have wave-particle duality. It was a key moment in quantum mechanics and confirmed de Broglie’s idea of matter waves.

The glancing angle $\theta$ is given as $\theta +\varphi +\theta =180^{\circ }$

$\theta =90^{\circ }-\frac{1}{2}\varphi =90^{\circ }-25^{\circ }=65^{\circ }$

For interatomic separation for Nickel crystal $d=0.914\mathring{A}$

For value of first order n=1 diffraction maximum,by using Bragg Law

$2d\sin \theta =\lambda$

$\lambda =2\times 0.914\times \sin 65^{\circ }=1.65\mathring{A}$

According to de-Broglie hypothesis the wavelength associated with an electron beam accelerated through 54 V is given as

$\lambda =\frac{h}{mv}=\frac{12.3}{\sqrt{V}}\mathring{A}=\frac{12.3}{\sqrt{54}}\mathring{A}=1.66\mathring{A}$