Define an atomic orbital.

An atomic orbital is a region in space around an atom's nucleus where an electron is most likely to be found. It is defined by a mathematical function called a wave function that describes the probabilities of the electron's location in three-dimensional space.

The atomic orbital can be characterized by three quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (m). Each quantum number represents a different aspect of the orbital's shape, size, and orientation. 1. Principal quantum number (n): This integer value determines the size and energy of the orbital, with higher n values corresponding to larger orbitals with higher energy levels. 2. Azimuthal quantum number (l): This integer value represents the shape of the orbital, with values ranging from 0 to n-1. Common shapes include s (spherical), p (dumbbell), d (cloverleaf), and f (complex) orbitals. 3. Magnetic quantum number (m): This integer value ranges from -l to +l, and determines the orientation of the orbital in space with respect to the nucleus.

The wave function (ψ) representing an atomic orbital helps us describe the electron cloud's spatial distribution. The square of the wave function, also known as the probability density (|ψ|^2), represents the probability of finding an electron in a specific region of space. The larger the value of |ψ|^2, the higher the likelihood of locating an electron in that area.

Based on the azimuthal quantum number (l), atomic orbitals can be classified into four primary types: 1. s orbitals (l = 0): Spherical-shaped orbitals that are symmetric around the nucleus. 2. p orbitals (l = 1): Dumbbell-shaped orbitals with nodes (regions of zero probability) at the nucleus. 3. d orbitals (l = 2): Cloverleaf-shaped orbitals with more complex shapes and multiple nodes. 4. f orbitals (l = 3): More complex orbitals with even more intricate shapes and numerous nodes.