Orbital angular momentum

Definition

Orbital angular momentum is a measure of the rotational motion of an electron around the nucleus in an atom. It is quantized and represented by quantum numbers.

5 Must Know Facts For Your Next Test

1. Orbital angular momentum is quantized and described using the azimuthal quantum number $l$.
2. The magnitude of orbital angular momentum is given by $\sqrt{l(l+1)}\hbar$, where $\hbar$ is the reduced Planck constant.
3. For a given principal quantum number $n$, the azimuthal quantum number $l$ ranges from 0 to $n-1$.
4. Each value of $l$ corresponds to a specific orbital shape (e.g., s, p, d, f orbitals).
5. The magnetic quantum number $m_l$, which ranges from $-l$ to $+l$, describes the orientation of the orbital angular momentum in space.

Review Questions

• What is the relationship between the azimuthal quantum number $l$ and the shape of atomic orbitals?
• How does one calculate the magnitude of orbital angular momentum for a given azimuthal quantum number $l$?
• What are the possible values of $l$ for an electron in an energy level with principal quantum number $n = 3$?

Related terms

Azimuthal Quantum Number: A quantum number for an atomic orbital that determines its orbital angular momentum and describes its shape.

Principal Quantum Number: A quantum number denoted by $n$, indicating the relative size and energy level of an atomic orbital.

$m_l$ (Magnetic Quantum Number): A quantum number associated with each value of $l$, describing the orientation of an orbital’s angular momentum in space; it ranges from -$l$ to +$l$.