Niels Bohr stipulated that electrons circled the nucleus in fixed orbitals, giving way to the common perception that electrons have set orbital paths, looking almost like the moon orbiting Earth. After the discovery of particle-wave duality, many scientists sought to determine how exactly the electrons behaved around the nucleus and how to precisely describe that behavior with mathematics. The Austrian Theoretical Physicist Erwin Schrödinger had a major breakthrough, describing electrons in terms of waves circling the nucleus. The electrons have energy levels that are spread out evenly into a spherical ‘cloud’, wherein the large percentage of the atoms electrons are positioned. Once one starts thinking in terms of such small scales such as that of an electrons size, Heisenberg/s Uncertainty principle comes into play. It states that the more you try to pinpoint the position of a body, the lower your precision becomes when measuring its momentum at that time, and vice-versa. Schrödinger then knew that the position of an electron could never really be precisely measured, as this act would effect the momentum of the electron, causing him to offer a more probabilistic approach to where the electrons positions were. It was named the electron cloud because it was where Schrödinger calculated there to be an overwhelming majority of the electrons of the atom located within its space.
Wave Mechanics and the Schrödinger Equation
Erwin Schrödinger knew that the idea of electrons behaving like wave forms would make it necessary to formulate ideas combining the ideas of electrons energy levels and the mechanics of waves. From this discovery, Schrödinger theorized that electron orbitals exist only in certain sizes, wherein an integral number of wavelengths can occupy that orbit, resulting in a standing wave where the wave continues to repeat itself as it goes around and then falls on itself. If the electron gains a little energy, the wavelength ends up decreasing, making it evident that a precise amount of energy must be gained or lost for there to be an integral number wavelengths within the orbit. Schrödinger then discovered that there was a point where so much energy is lost, wherein the wavelength increases to the extreme where only a single wavelength can fit in the orbit, and this is called the ground state. The energy that maintains standing waves through emission or absorption is known as quanta, giving way to the coining of the now gargantuan and fearful title of quantum mechanics. In 1926, Schrödinger formulated an equation to describe how the quantum state of a physical system changes through time, calling it the Schrödinger equation, and making it the foundation of wave mechanics.