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Spin angular momentum Calculator

Magnitude of intrinsic spin angular momentum.

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Formula first

Overview

Spin angular momentum has the same ħ sqrt(s(s+1)) structure as any other quantum angular momentum.

Symbols

Variables

S = S

S
Variable

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 a particle has a spin quantum number s = 1, what is the value of the term s(s + 1) used to calculate the magnitude of the spin angular momentum?

Solve for:

Hint: Plug s = 1 into the expression s(s + 1).

The full worked solution stays in the interactive walkthrough.

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. Wikipedia: Spin (physics)
  7. Griffiths, David J. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press.
  8. Landau, L. D., & Lifshitz, E. M. (1977). Quantum Mechanics: Non-Relativistic Theory (Vol. 3). Pergamon Press.