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Spin-orbit coupling Calculator
Allowed j values from spin-orbit coupling.
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Formula first
Overview
Spin-orbit coupling combines orbital and spin angular momentum into allowed total-j values.
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
If an electron has an orbital angular momentum quantum number l = 1, what are the possible total angular momentum quantum numbers j?
Solve for:
Hint: Recall that j = l ± s, where s = 1/2 for an electron.
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
- Griffiths, David J. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press.
- Atkins, Peter; de Paula, Julio (2017). Physical Chemistry (11th ed.). Oxford University Press.
- Landau, L. D., & Lifshitz, E. M. (1977). Quantum Mechanics: Non-Relativistic Theory (Vol. 3, 3rd ed.). Pergamon Press.
- Sakurai, J. J., & Napolitano, J. (2017). Modern Quantum Mechanics (2nd ed.). Cambridge University Press.