The Rutherford Gold Foil Experiment was conducted in 1911 by Hans Geiger and Ernest Marsden. It Involved shooting alpha particles (He nuclei) at a gold foil to observe how they are scattered by the gold on a screen. It probed the structure of the Atom.
If atoms were a solid mass few if any alpha particles would get through. If negative electron were embedded in a thin positive mass all of the alpha particles would get through. However most of the alpha particles get through with some being scattered by the small positive nucleus. Rutherford Conclusion was that the atoms is mostly empty space with a small positive nucleus surrounded by electrons scattered through out the surrounding space. In such a model the electron can not stand still since if they did they fall into the nucleus
This led to efforts to model the atom as a solar system called the planetary model with electrons orbiting the nucleus like planets around a star. The problem with the planetary model is that electrons are charged particles and an accelerating charge emits light loosing energy and this would cause the electron to spiral into the nucleus.
Broglie had shown that particles have wave like propertied. Bohr went on to show that these waves could be bent into orbits like those expected for an electron with the result that electrons can only occupy those orbits with exactly a whole number of wavelengths. In these orbits the waves are add together with constructive interference. If an orbit has a fractional number of wavelengths the wave would destructively interfere and not persist so an electron can not occupy such an obit. The result is that that electrons jump from orbit to orbit emitting photons when going to a lower orbit and absorbing photons are when going to a higher orbit. It turns out that transitions between the possible electron orbits, matches the spectral lines that are actually observed in hydrogen. This was a major step in development quantum Mechanics.
Studying elements other hydrogen included the effects of multiple electrons resulted in the electron orbital five of which are shown above. They are places in an atom where electrons can actually be found. The shapes of these orbitals were originally found mathematically and they have long been viewed as purely mathematical abstractions that were never expected to be seen. Physics students have long been told this however field-emission electron microscopy has changed this. he imaging of actual electron orbitals was a surprise but it vividly shows the accuracy of Quantum Mechanics.