Yes, electrons indeed exhibit wave-like properties when they are fired one by one through a double-slit experiment. The double-slit experiment is a classic experiment that demonstrates the wave-particle duality of matter, including electrons.
In the double-slit experiment, a beam of electrons is directed towards a barrier with two narrow slits. Behind the barrier, a screen or detector is placed to observe the pattern formed by the electrons that pass through the slits.
If electrons were purely particles, one would expect them to create two distinct bands on the screen, corresponding to the two slits. However, what actually happens is that even when electrons are sent through the experiment one by one, over time, an interference pattern emerges on the screen. This interference pattern consists of alternating bright and dark bands, similar to the pattern observed when light waves pass through the slits.
The appearance of the interference pattern indicates that the electrons are behaving as waves. This phenomenon can only be explained if we consider that each electron goes through both slits simultaneously and interferes with itself, creating the interference pattern on the screen.
This experiment, along with other similar experiments involving particles such as electrons, protons, and even larger molecules, highlights the wave-particle duality inherent in quantum mechanics. It shows that particles like electrons can exhibit wave-like behavior, emphasizing the non-intuitive nature of the microscopic world.