In classical physics there are two well differentiated worlds: waves (mechanical or electromagnetic) and particles (corpuscles), both very well defined.
In classical physics there are two well differentiated worlds: waves (mechanical or electromagnetic) and particles (corpuscles), both very well defined.
It was previously thought that there was no relationship between these two worlds, but at the end of the 19th century, as the small world (molecules, atoms and their components) became known, it was discovered that the smallest particles could behave like waves. If the particles behaved like waves, we had to know what the wave associated with those particles was: the “particle wave”.
Read more: Einstein’s relativity also forces us to redefine the concept of mass
At the same time, at that time the opposite was revealed: a wave behavior similar to that of particles. Two examples are the photoelectric effect and the Compton effect.
Luis De Broglie was based on the definition that already existed of photons: that they were the particles that make up light (in classical physics, a wave) that behaved like particles. Thus, it was known that the mass of photons was zero, that their speed was that of light and that they had an impulse associated with the wavelength of that light (wavelength is a characteristic of waves that tells us to how far the wave repeats itself).
De Broglie thought that if light could behave like a particle and have a momentum associated with its wavelength, electrons could behave like waves, and have a wavelength associated with its momentum.
He defined the de Broglie wavelength, “the wave of the particle,” as Planck’s constant (a very small number characteristic of the atomic world) divided by the momentum of the particle.
This idea was not based on any calculation or on any evidence. It was a hypothesis that had to be proven.
The double slit experiment for light
The double slit experiment is an experiment carried out in the early 19th century by the English physicist Thomas Young, with the aim of supporting the theory that light was a wave and rejecting the theory that light was made up of particles.
Young shone a beam of light through two slits and saw a pattern of interference appear on a screen, a series of alternating bright and dark stripes.
This result is inexplicable if the light were made up of particles because only two fringes of light should be observed in front of the slits, but it is easily interpretable assuming that the light is a wave and that it suffers interference.
Later this experiment has been considered in quantum physics to demonstrate the wave behavior of very small particles, on the scale of atoms. The experiment can be performed with electrons, atoms or neutrons, producing interference patterns similar to those obtained when performed with light. This therefore shows this wave behavior of the particles.
The double slit experiment for electrons
Let’s see what happens in the double slit experiment if instead of a light beam we have an electron beam.
These electrons can be launched with any speed we want, accelerating them through a difference in electrical potential. Since we can choose the speed of these electrons and the de Broglie length depends on the speed, we are actually choosing the wavelength of these electrons.
However, the construction of a double slit in the case of electrons is not easy at all. It was not until many years after the idea was proposed that this experiment could be carried out.
In 1961, Claus Jönsson accelerated an electron beam through 50,000 volts and passed this beam through a double slit with very small spacing and width.
The electron beam was first passed through a single slit and counted at a distance with detectors. The detectors in front of the slit counted many more electrons.
Then another slit was made, with which it was seen that a few maximums and minimums of electron counts appeared according to the position of the detectors.
That is, there were detectors at the height of the first slit that received fewer electrons when there were two slits than when there was one.
The first thing they thought is that it was because of the charge that the electrons had. Being negatively charged, these electrons could repel each other as they traveled together in the beam. To verify this, they launched electrons one by one with the two open slits and the same result was obtained, for which they came to the conclusion that these maxima and minima indicated that the electrons had suffered interference and, therefore, had wave properties.
The double-slit interference pattern photographed by Jönsson was similar to the double-slit patterns obtained with light sources, reinforcing the evidence in favor of the wavelike nature of the particles.
At the same time, other experiments were done with particles that reached the same conclusion: they had wave properties. This was not explicable from the point of view of classical physics, so it would be part of a large branch of modern physics, quantum physics.
The impossible to measure experiment
Let us estimate the de Broglie wave associated with the electron. If the electron is moving with a speed close to that of light, for example 0.6 times the speed of light, its associated wavelength is approximately 3 picometers, a very small but measurable wavelength, within the spectrum of X or gamma rays.
Now, let’s calculate the de Broglie wavelength of a car that weighs 1000 kg and is moving at a speed of 100 meters per second. The wavelength associated with this car is 6.6 x 10⁻³⁹ m, which is so small that it is impossible to measure.
Therefore, there is no experiment that can show the wave nature of macroscopic objects. Only when one penetrates inside the atom to do experiments with atomic and nuclear particles is it possible to observe the de Broglie wavelength, the wavelength of the particles. (I)
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