Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.

The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the 1s orbital. This orbital can hold two electrons. The next shell holds eight total electrons: two in the spherical 2s orbital and two in each of the three dumbbell-shaped 2p orbitals. The higher energy levels are the outermost orbitals—those found in the d and f subshells— that take on more complex shapes. A total of 10 electrons can fit within the five d orbitals, and 14 total electrons fit within the seven f orbitals. The s subshell has the lowest amount of energy. Electrons in the p subshell have higher energy, followed by the d and f subshell if they are present. Orbital diagrams can be used to visualize the location and relative energy levels of each electron in an atom.

The concept of orbitals was introduced by the Bohr Model. In 1913, Niels Bohr was able to experimentally determine how much energy was gained and lost when electrons changed orbitals in an atom of hydrogen and other ions with a single electron. Combining the results of his experiments with prior knowledge of a positively-charged nucleus from the work of Ernest Rutherford, Bohr developed the first model of electron orbitals. When electrons gain energy, they enter an excited state and jump to higher orbitals. Energy can be added to electrons in the form of heat or light, and when they lose that energy rapidly, they fall back from the higher orbital and emit a particle of light called a photon. The color of the emitted photon corresponds to a specific amount of energy that can be quantified by a spectroscope.

Bohr's model of electron orbitals assumed that electrons orbited the nucleus in fixed circular paths. While his experiments were accurate for hydrogen and hydrogen-like ions with a single electron, he could not predict the electron configurations of other elements. In 1926, Erwin Schrödinger expanded Bohr's model of energy levels and developed the model of atomic orbitals that is still accepted today. Schrödinger took a number of other discoveries into account regarding the physical behavior of electrons that were made by scientists in the early 1920s. His quantum mechanical model accurately predicts the electron configurations of elements with multiple electrons. One fundamental change in Schrödinger's model is the assumption that electrons travel in a wave motion that is affected by the positive charge of the nucleus. Because of this, the orbitals that we speak of today are cloud-like areas where electrons are most likely to be found rather than fixed circular paths as Bohr proposed.