The azimuthal quantum number (often denoted as “l”) is one of the quantum numbers used to describe the properties of electrons in atoms and their distribution within atomic orbitals. It defines the shape and subshell of an orbital and provides information about the angular momentum of an electron’s motion around the nucleus.

Key points about the azimuthal quantum number:

1. Values: The azimuthal quantum number can take integer values ranging from 0 to (n-1), where “n” is the principal quantum number. Thus, for a given principal quantum number (shell), the azimuthal quantum number can take values from 0 to (n-1).
2. Subshells: The azimuthal quantum number defines the subshells within each energy level (shell). Each subshell corresponds to a specific value of “l” and has a different shape.
3. Orbital Shapes: Different values of the azimuthal quantum number determine the shape of the orbital. For example, when l = 0, the orbital is an s orbital with a spherical shape. When l = 1, the orbital is a p orbital with a dumbbell shape along a specific axis.
4. Number of Subshells: The number of subshells within a given shell is equal to the value of “n.” For example, the first shell (n = 1) has one subshell (l = 0), the second shell (n = 2) has two subshells (l = 0 and l = 1), and so on.
5. Number of Orbitals: For a given value of “l,” there are (2l + 1) possible magnetic quantum number (m) values. Each magnetic quantum number corresponds to an orbital with a specific orientation in space.
6. Electron Capacity: The number of electrons that can be accommodated in a subshell is given by (2l + 1), which represents the total number of orbitals in that subshell.
7. Energy Order: Subshells with different values of “l” have different energy levels. The energy increases as the value of “l” increases within the same principal quantum level (n).
8. Subshell Labels: Subshells are often labeled using letters: s for l = 0, p for l = 1, d for l = 2, and f for l = 3.

The azimuthal quantum number, along with the principal quantum number (n) and other quantum numbers (m and s), helps define the detailed electronic structure of atoms and the arrangement of electrons within orbitals and subshells. It plays a crucial role in understanding atomic properties and behavior, as well as the periodic table.