The azimuthal quantum number (also known as the orbital angular momentum quantum number) is denoted by the symbol ℓ (lowercase "ell") and is one of the four quantum numbers used to describe the electron orbitals in an atom. It determines the shape of the electron's orbital.
The azimuthal quantum number depends on the principal quantum number (n). The principal quantum number, denoted by the symbol n, describes the energy level or shell of the electron. It specifies the average distance of the electron from the nucleus.
The azimuthal quantum number (ℓ) can take integer values ranging from 0 to (n-1). In other words, for a given value of n, the range of ℓ would be 0, 1, 2, ..., (n-1).
The relationship between the principal quantum number (n) and the azimuthal quantum number (ℓ) is that each principal energy level (n) can have sublevels (orbitals) with different shapes corresponding to different values of ℓ. For example:
- When n = 1, there is only one possible value for ℓ, which is ℓ = 0. This corresponds to the s orbital, which is spherical in shape.
- When n = 2, there are two possible values for ℓ: ℓ = 0 corresponds to the 2s orbital, and ℓ = 1 corresponds to the 2p orbitals, which have a dumbbell-like shape.
- When n = 3, there are three possible values for ℓ: ℓ = 0 corresponds to the 3s orbital, ℓ = 1 corresponds to the 3p orbitals, and ℓ = 2 corresponds to the 3d orbitals, which have more complex shapes.
In summary, the azimuthal quantum number (ℓ) depends on the principal quantum number (n) and determines the shape of the electron's orbital within a given energy level or shell.