An atom’s magnetic moment comes from both electron spin and orbital motion. The Landé g-factor combines them and explains how spectral lines split in a magnetic field (the Zeeman effect).
How to use the Magnetic Moment Calculator
- Spin quantum number S
- Orbital quantum number L
- Total angular momentum J
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter S, L and J (half-integers allowed, e.g. 2.5).
Inputs explained
| Field | What to enter |
|---|---|
| Spin quantum number S | A number |
| Orbital quantum number L | A number |
| Total angular momentum J | A number |
What each result means
- Landé g-factor g_J = 1 + ([Total angular momentum J]×([Total angular momentum J] + 1) + [Spin quantum number S]×([Spin quantum number S] + 1) – [Orbital quantum number L]×([Orbital quantum number L] + 1))÷(2×[Total angular momentum J]×([Total angular momentum J] + 1))
- Effective moment = [Landé g-factor g_J]×sqrt([Total angular momentum J]×([Total angular momentum J] + 1))
- In J/T = [Effective moment]×9.2740100783e-24
Example values
How the main result changes when Spin quantum number S changes and everything else stays at the example values above:
| Spin quantum number S | Landé g-factor g_J |
|---|---|
| 1.25 | 1.6607 |
| 1.88 | 1.808 |
| 2.5 | 2 |
| 3.13 | 2.2366 |
| 3.75 | 2.5179 |
| 5 | 3.2143 |
Formula
g_J = 1 + [J(J+1) + S(S+1) − L(L+1)] / [2J(J+1)], μ_eff = g_J·√(J(J+1))·μ_B
Worked example
Inputs — Spin quantum number S: 2.5; Orbital quantum number L: 0; Total angular momentum J: 2.5.
Results — Landé g-factor g_J = 2; Effective moment = 5.91608 μ_B; In J/T = 5.4866e-23 J/T; Check |L − S| ≤ J ≤ L + S = Valid combination.
Key terms
- Landé g-factor
- Ratio of magnetic moment to angular momentum.
Frequently asked questions
What is g for a pure spin?
About 2 (L = 0).
What is g for pure orbital motion?
1 (S = 0).
What is Mn²⁺'s moment?
S = 5/2, L = 0 → 5.92 μ_B.
What is the Zeeman effect?
Splitting of levels in a magnetic field, proportional to g_J.