F orbital

In quantum mechanics, an f orbital is one of the types of orbitals in atoms used to describe the distribution of electrons around the nucleus. The "f" in f orbital stands for "fundamental". These orbitals are characterized by their high angular momentum, represented by the quantum number \(l = 3\). The shape of f orbitals is more complex than the s, p, and d orbitals, featuring intricate, multi-lobed structures.

F orbitals come into play for elements in the lanthanides and actinides series of the periodic table, starting from the element cerium (atomic number 58) onwards, where electrons begin to fill the 4f subshell, and from thorium (atomic number 90) where they start to fill the 5f subshell. The presence of electrons in f orbitals significantly influences the chemical properties and magnetic properties of these elements.

Each f subshell can hold up to 14 electrons, as there are seven f orbitals (magnetic quantum number \(m_l\) can take values from -3 to +3), and each orbital can hold two electrons with opposite spins. The shapes of these orbitals are complex, with lobes pointing in different directions and often containing a ring or torus of electron density. This complexity arises from the orbital's angular momentum and the Pauli exclusion principle, dictating that no two electrons can have the same set of quantum numbers within an atom.

Understanding f orbitals is crucial for explaining the chemistry of the lanthanides and actinides, including their color, magnetic behavior, and the formation of compounds. Their complex nature also makes them a subject of interest in advanced materials science, particularly in the development of magnetic and luminescent materials.