Understanding Magnetic Quantum Numbers

The magnetic quantum number, denoted as $m_l$, describes the orientation of an atomic orbital in space relative to an external magnetic field. It is related to the angular momentum quantum number, $l$.

Analyzing p Orbitals

For p orbitals, the angular momentum quantum number $l$ is equal to 1.

• The possible values for the magnetic quantum number $m_l$ range from $-l$ to $+l$, including 0.
• Therefore, for $l=1$, the possible values of $m_l$ are -1, 0, and +1.
• These three values correspond to the three degenerate p orbitals: $p_x$, $p_y$, and $p_z$.

Determining the Value for $p_x$

Conventionally, the three p orbital orientations are assigned specific $m_l$ values:

• The $p_z$ orbital is typically associated with $m_l = 0$.
• The $p_x$ and $p_y$ orbitals correspond to the orientations along the x and y axes. They are associated with the remaining $m_l$ values, which are -1 and +1.

However, there is no fixed rule stating that $p_x$ *must* be assigned +1 and $p_y$ *must* be assigned -1 (or vice versa). The assignment of +1 and -1 to $p_x$ and $p_y$ is a matter of convention and can be interchanged.

Since the designation "$p_x$" does not uniquely correspond to a single, specific numerical value of $m_l$ (it could be either +1 or -1 depending on the convention used), the value is considered 'undefined' when a single definitive answer is required solely based on the orbital label.