Orbitalzustände

Orbitalzustände, also known as atomic orbitals, describe the regions of space around an atom's nucleus where there is a high probability of finding an electron. These are not physical paths electrons follow, but rather mathematical functions derived from the Schrödinger equation. Each orbital is characterized by a set of quantum numbers that define its energy, shape, and orientation in space.

The principal quantum number, denoted by 'n', describes the electron's energy level and the average distance of the electron from the nucleus. Higher values of 'n' indicate higher energy levels and greater distances. The angular momentum quantum number, 'l', determines the shape of the orbital. 'l' can take integer values from 0 to n-1. These shapes are commonly referred to by letters: 's' orbitals are spherical (l=0), 'p' orbitals are dumbbell-shaped (l=1), 'd' orbitals have more complex shapes (l=2), and 'f' orbitals have even more intricate forms (l=3).

The magnetic quantum number, 'm_l', specifies the orientation of the orbital in three-dimensional space. For a given 'l', 'm_l' can range from -l to +l, including 0. For example, 'p' orbitals (l=1) have three possible orientations: along the x, y, and z axes. Finally, the spin quantum number, 'm_s', describes the intrinsic angular momentum of the electron, which has two possible values, +1/2 and -1/2, often referred to as "spin up" and "spin down."

Electrons in an atom occupy these orbitals according to specific rules, such as the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers, and Hund's rule, which dictates that electrons will fill orbitals of the same energy singly before pairing up. The arrangement of electrons in these orbitalzustände dictates an atom's chemical properties and bonding behavior.