There are several types of atomic orbitals, each characterized by a specific shape, orientation, and energy level. These orbitals define the regions in space around the nucleus where electrons are likely to be found. The types of orbitals include:

1. s Orbitals (Sharp): Spherical in shape, s orbitals have no nodal planes (regions where the probability of finding an electron is zero). They are centered on the nucleus. As the principal quantum number (n) increases, the size of the s orbital also increases.
2. p Orbitals (Principal): P orbitals are dumbbell-shaped and come in three orientations: px, py, and pz. Each p orbital has a nodal plane perpendicular to its axis. P orbitals have two lobes on opposite sides of the nucleus. There are three p orbitals in each energy level.
3. d Orbitals (Diffuse): D orbitals have more complex shapes and come in five different orientations (dxy, dyz, dz2, dxz, dx2-y2). These orbitals have nodal planes and angular nodes. There are five d orbitals in each energy level.
4. f Orbitals (Fundamental): F orbitals have even more complex shapes and come in seven different orientations. They have multiple nodal planes and angular nodes. F orbitals are found in higher energy levels and are not as commonly encountered.

The arrangement and energy of these orbitals are described by the principal quantum number (n), azimuthal quantum number (l), and magnetic quantum number (m). The number of possible orbitals increases with higher energy levels. Electrons occupy these orbitals in accordance with the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of quantum numbers.

The various orbitals contribute to the overall electronic structure and geometry of atoms and molecules. For example, s and p orbitals are often involved in forming chemical bonds, while d and f orbitals play roles in more complex interactions and transition metal chemistry.