Atomic orbitals are regions of space around the nucleus of an atom where electrons are most likely to be found. They describe the probability of finding an electron within a specific energy level and shape within an atom.
Electron shells refer to the energy levels in an atom where electrons can exist. Atomic orbitals, on the other hand, describe the specific shapes and orientations of the electron clouds within those energy levels.
The number of atomic orbitals in an atom depends on the energy level. The first energy level, or shell, has one orbital, while the second and third energy levels have 4 and 9 atomic orbitals, respectively. In general, the number of atomic orbitals in an energy level is equal to n^2, where n is the energy level number.
The letters s, p, d, and f refer to the shape of the atomic orbitals. The s orbital is spherical, while the p orbital is dumbbell-shaped. The d orbital has a cloverleaf shape, and the f orbital has a more complex shape with multiple lobes. Each orbital can hold a different number of electrons and has a unique energy level.
Electrons fill atomic orbitals according to the Aufbau principle, which states that electrons will fill the lowest energy orbitals first before moving to higher energy levels. This rule is also known as the "building-up" principle. Additionally, the Pauli exclusion principle and Hund's rule dictate how electrons are distributed within the orbitals.