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The wave-particle duality of electrons and other particles is a fundamental concept in quantum mechanics. It describes the behavior of particles like electrons, which can exhibit both wave-like and particle-like properties depending on how they are observed or measured.

The discovery of the wave-like behavior of electrons came about through a series of experiments in the early 20th century. One of the most famous experiments demonstrating this duality is the double-slit experiment, which was initially conducted with light but later extended to electrons and other particles.

In the double-slit experiment, a beam of particles, such as electrons, is directed towards a barrier containing two narrow slits. Behind the barrier, a screen is placed to detect the particles. When particles pass through the slits and hit the screen, an interference pattern emerges, similar to what is observed with waves, such as water waves or light waves.

This interference pattern suggests that the particles are behaving like waves and interfering with themselves. However, when the experiment is modified to detect which slit each particle passes through (by placing detectors or measuring devices), the interference pattern disappears, and the particles behave more like individual particles, creating a pattern resembling two separate distributions.

The crucial point here is that the act of observation or measurement itself affects the behavior of the particles. The presence of detectors or measurement devices disrupts the wave-like behavior and forces the particles to behave more like particles with definite positions.

Based on these and similar experiments, scientists have concluded that particles, including electrons, can exhibit both wave-like and particle-like properties. The behavior observed when the particles are not measured suggests wave-like characteristics, while the behavior observed when measurement occurs indicates particle-like characteristics.

It's important to note that scientists don't observe electrons directly as waves. Instead, they observe the outcomes of experiments and measurements, which provide evidence for the wave-like behavior. The wave-particle duality arises from the mathematical framework of quantum mechanics, which successfully describes the behavior of particles at the microscopic level.

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