Angular momentum quantum number

Definition

The angular momentum quantum number, denoted by $l$, determines the shape of an electron's orbital and its orbital angular momentum. It can take any integer value from 0 to $n-1$, where $n$ is the principal quantum number.

5 Must Know Facts For Your Next Test

1. The angular momentum quantum number $l$ can have integer values ranging from 0 to $n-1$.
2. For a given principal quantum number $n$, the possible values of $l$ are 0, 1, 2, ..., $(n-1)$.
3. $l=0$ corresponds to an s-orbital, $l=1$ to a p-orbital, $l=2$ to a d-orbital, and so on.
4. The total number of orbitals for a given energy level is determined by summing $(2l + 1)$ for all possible values of $l$.
5. The value of the angular momentum quantum number affects the magnetic quantum number ($m_l$), which ranges from $-l$ to $+l$.

Review Questions

• What is the range of possible values for the angular momentum quantum number when the principal quantum number is 3?
• How does the value of the angular momentum quantum number affect the shape of an electron's orbital?
• What are the allowed values of $m_l$ if the angular momentum quantum number is 2?

Related terms

Principal Quantum Number: Denoted by $n$, it specifies the energy level of an electron in an atom and determines its average distance from the nucleus.

Magnetic Quantum Number: Denoted by $m_l$, it specifies the orientation of an orbital around the nucleus and can take values ranging from $-l$ to $+l$, including zero.

Spin Quantum Number: $s$, indicates the intrinsic spin of an electron with possible values of +1/2 or -1/2.