# Electron diffraction and De Broglie hypothesis

The French physicist Louis De Broglie in the 1920s assumed that the same duality light have can be applied to all other forms of matter.

More specifically, he believed that all types of microparticles (for example, electrons) also have wave properties. They can show the phenomena of interference, diffraction, etc. It was a time when the dual nature of electromagnetic radiation – corpuscular and wave – had already been established. Electron diffraction is a phenomenon that is consistent with De Broglie’s hypothesis and confirms the dual nature of electrons.

According to the hypothesis, each cell is accompanied by a wave, De Broglie’s wave, whose wavelength can be determined from the pulse of the cell.

It is a lot about any kind of waves known until then (acoustic, electromagnetic, etc.), but about a completely new quantum appears.

The wavelength of De Broglie’s waves are shorter the higher the mass and velocity of the particle.

## Electron diffraction experiment

The existence of particle waveforms is the first experiment proved by Davisson and Germer in 1927.

Electron diffraction was proven experimentally. They observed the spatial distribution of electrons reflected from the surface of nickel crystals. Furthermore, they observed the number of ejected electrons that depends on the scattering angle, namely the lattice.

A new phenomenon has been discovered in the same way as the diffraction of X-rays by crystalline electron diffraction. De Broglie wavelength can be determined by analysis of diffraction images (diffractograms) obtained on a known crystal lattice electrons. The obtained values exactly match the values calculated.

This gave De Broglie’s hypothesis complete confirmation. Electron diffraction is used to examine the structure of a material similar to X-ray diffraction.

We use Electron diffraction to examine the structure of a material similar to X-ray diffraction. Electron microscopy has found even wider application. It is also based on the wave properties of particles. An optical microscope uses light and glass lenses to obtain the shape of an object.

On the other hand, an electron microscope uses an electron beam and electrostatic or electromagnetic lenses. In the first case, cylindrical capacitors serve as lenses, and in the second, electromagnets of a special shape. The advantage of electron microscopes over optical ones is that they work at much shorter wavelengths. For example, 0.005 nm instead of 500 nm. Therefore it has a much better decomposition power, smaller objects can be observed.

The magnification of modern electron microscopes is up to about a million times.

### De Broglie’s waves

The discovery of De Broglie’s waves had a great practical significance. Also a huge influence on the further development of modern physics.

With this discovery, the development of quantum mechanics began. Without De Broglie’s hypothesis, it is impossible to correctly describe electron diffraction in the microworld.

The question is, what is the nature of De Broglie’s waves?

These waves have no analogy in classical physics but represent a specific quantum concept. De Broglie’s waves have the physical meaning of “probability waves.” The intensity is a measure of the probability that the particles will be found at a given point in space.

Using these waves, we can calculate, for example, what is the probability that an electron of a given velocity will scatter on the crystal in a certain direction and find the places of the greatest blackening in the diffraction image.

It does not mean that all electrons will fall in those places. There is always some “blurring” of the diffraction image, which is not the result of imperfection of the measuring apparatus but originates from the wave nature of the phenomenon itself.

The same is the case, for example, with electron orbits “in an atom” – these are not strictly defined paths (like planetary orbits), but only the most probable places where electrons are found in an atom.