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