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Total angular momentum Calculator
Magnitude of total angular momentum.
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Formula first
Overview
The magnitude of the total angular momentum is ħ sqrt(j(j+1)).
Symbols
Variables
J = J
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
How does the magnitude of the total angular momentum scale as the quantum number j increases?
Solve for:
Hint: Look at the formula J = ħ√j(j+1).
The full worked solution stays in the interactive walkthrough.
References
Sources
- Chemistry LibreTexts, hydrogen atom, angular momentum, and bonding orbitals chapters, accessed 2026-04-09
- Chemistry LibreTexts, bonding and antibonding orbitals, accessed 2026-04-09
- Chemistry LibreTexts, angular momentum in the hydrogen atom, accessed 2026-04-09
- NIST CODATA
- IUPAC Gold Book
- Atomic and molecular orbital - Wikipedia
- Griffiths, David J. Introduction to Quantum Mechanics
- Sakurai, J. J., & Napolitano, Jim. Modern Quantum Mechanics