User:Imanj11/sandbox

Davisson and Germer experiment
The Davisson–Germer experiment was a physics experiment conducted by American physicists Clinton Davisson and Lester Germer in 1927, which confirmed the de Broglie hypothesis. The de Broglie hypothesis, a theory advanced by Louis De Broglie in 1924, says that particles of mattersuch as electrons in this experiment have wave like properties. The experiment not only played a major role in verifying the de Broglie hypothesis and demonstrated the wave-particle duality but also was an important historical development in the establishment of quantum mechanics and of the Schrödinger equation

History and Overview
According to Maxwell's equations in the late 19th century, light was thought to consist of waves of electromagnetic fields and matter consist of localized particles. However this was challenged in Albert Einstein’s 1905 paper on the Photoelectric effect which described light comprising of discrete and localized quanta of light (now called photons) that won him the Nobel Prize in Physics in 1921. In 1927 Louis de Broglie presented his thesis concerning the wave-particle duality theory, proposing the idea that all matter displayed the wave-particle duality of photons. According to the de Broglie for all matter and for radiation alike, the energy E of the particle was related to the frequency of its associated wave v by the Planck relation:
 * $$E=h\nu\,$$

And that the momentum of the particle p was related to its wavelength by what is now known as the de Broglie relation:
 * $$p=\frac{h}{\lambda},$$

Where h is Planck's constant.

An important contribution to the Davisson-Germer experiment was Walter M. Elsasser, while in Gottingen in the 1920s, he remarked that the wave-like nature of matter might be investigated by electron scattering experiments on crystalline solids, as the wave-like nature of X-rays was confirmed through X-ray scattering experiments on crystalline solids.

This suggestion of Elsasser was then communicated by his senior colleagues (Nobel Prize recipient Max Born) to physicists in England. When the Davisson and Germer experiment was performed, the results of the experiment were explained by Walter M. Elsasser proposition. It should be noted that the formal intention of the Davisson and Germer experiment was not aimed to confirm the de Broglie hypothesis, but it was intended to study the surface of nickel.

In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline nickel target. The angular dependence of the reflected electron intensity was measured and was determined to have the same diffraction pattern as those predicted by Bragg for X-rays. This experiment was also replicated by George Paget Thomson independently at the same time and for which Thompson was jointly awarded and shared the Nobel Prize in Physics in 1937 with Clinton Joseph Davisson. The Davisson – Germer experiment confirmed the de Broglie hypothesis that matter displayed wave-like behavior. This, in combination with Arthur Compton’s experiment which won him the Nobel Prize for Physics in 1927 for the discovery of the Compton effect, established the wave –particle duality hypothesis for which it was a fundamental step in quantum theory.

Experiment
Davisson and Germers actual objective was to study the surface of a piece of nickel by directing a beam of electrons at the surface and observing how many electrons bounced off at various angles. They expected that for electrons even the smoothest crystal surface would be too rough and so the electron beam would experience diffuse reflection.

The experiment consisted of firing an electron beam from an electron gun directed to a piece of nickel crystal at normal incidence (i.e. perpendicular to the surface of the crystal). The setup of the experiment included an electron gun consisting of a heated filament that released thermally excited electrons. The thermally excited electrons that were released from the electron gun were then accelerated through a potential difference giving them a certain amount of kinetic energy towards the nickel crystal. To avoid bouncing of the electrons with other molecules on their way towards the surface, the experiment was conducted in a vacuum chamber. To measure the number of electrons that were scattered at that particular angle, an electron detector was used. The detector designed to accept only elastically scattered electrons and their near neighbours that could be moved on an arc path about the crystal.

But during the experiment an accident happened and air got into the chamber which led to an oxidfilm on the nickelsurface. To remove the oxid Davisson and Germer baked the specimen in a high temperature oven, not knowing that this effected the former polycristalline structure of the crystal to get large single crystal areas with crystalplanes continuous over the width of the electron beam.

When they started the experiment again and the electrons hit the surface, they were scattered by the originated planes of crystal-atoms inside the nickel crystal. As Max von Laue approved in 1912 the crystal structure serves as kind of a three dimensional diffraction grating. The angles of maximum reflection are given by Braggs condition for constructive interference from an array, Bragg's law
 * $$n\lambda=2d\sin \left(90^{\circ} -\frac{\theta}{2} \right),$$

for n = 1, θ = 50°, and for the spacing of the crystalline planes of nickel (d = 0.091 nm) obtained from previous X-ray scattering experiments on crystalline nickel.

By varying the applied voltage to the electron gun or accelerator, the maximum intensity of electrons diffracted by the atomic surface was found at different angles. The highest intensity was observed at an angle of θ = 50° with a voltage of 54 V, giving the electrons a kinetic energy of $54 eV$.

According to the de Broglie relation and Bragg's law, a beam of $54 eV$ had a wavelength of $0.165 nm$. The experimental outcome was $0.167 nm$, which closely matched the predictions.

Davisson and Germer accidentally discovered the diffraction of electrons, this was the first direct evidence confirming de Broglie's hypothesis that particles can have wave properties as well.