Z-Component of Orbital Angular Momentum Calculator

Formula first

Overview

The z-component of orbital angular momentum is quantized in integer steps of ħ.

Symbols

Variables

$L_z$ = $L_z$

Apply it well

When To Use

When to use: Use this when you need hydrogenic quantum numbers or simple bonding pictures for atoms and molecules.

Why it matters: These are the standard quantum-number rules behind shell filling, angular momentum, and orbital shapes.

Avoid these traps

Common Mistakes

• Confusing orbital orientation with orbital energy.
• Ignoring spin when counting the number of available states.
• Mixing up the magnitude of angular momentum with its z-component.

One free problem

Practice Problem

If the orbital angular momentum quantum number l is 2, what are the possible values for the magnetic quantum number $m_l$?

Solve for: $L_z$

Hint: Recall that $m_l$ ranges from -l to +l in integer steps.

The full worked solution stays in the interactive walkthrough.

Keep going

Related Formulas

References

Sources

1. Chemistry LibreTexts, hydrogen atom, angular momentum, and bonding orbitals chapters, accessed 2026-04-09
2. Chemistry LibreTexts, bonding and antibonding orbitals, accessed 2026-04-09
3. Chemistry LibreTexts, angular momentum in the hydrogen atom, accessed 2026-04-09
4. NIST CODATA
5. IUPAC Gold Book
6. Quantum Mechanics, by David J. Griffiths
7. Griffiths, David J. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press.
8. NIST Chemistry WebBook