Calculator Inputs
Example data table
This worked example shows a common anomalous setup for quick testing.
| Parameter | Example value | Notes |
|---|---|---|
| Magnetic field B | 1.2 T | Moderate laboratory field. |
| Rest wavelength | 589.0 nm | Visible yellow region. |
| Upper state (L, S, J) | (1, 0.5, 1.5) | Landé g ≈ 1.3333. |
| Lower state (L, S, J) | (0, 0.5, 0.5) | Landé g ≈ 2.0000. |
| Allowed components | 6 | Before grouping identical positions. |
| Largest |Δλ| | 32.3930 pm | Strongest blue or red offset. |
| Total spread | 64.7860 pm | From most blue to most red line. |
Formula used
Level shift: ΔE = μB B gJ mJ
Landé factor: gJ = 1 + [J(J+1) + S(S+1) − L(L+1)] / [2J(J+1)]
Transition shift: ΔEtransition = μB B (gumu − glml)
Frequency shift: Δν = ΔE / h
Shifted wavelength: λ′ = c / (ν0 + Δν), where ν0 = c / λ0
Wavenumber shift: Δσ = Δν / (c × 100), reported in cm-1
Allowed electric-dipole transitions satisfy Δm = 0, ±1 and ΔJ = 0, ±1, excluding the 0 → 0 case.
How to use this calculator
- Enter the magnetic field strength and the unshifted wavelength.
- Choose normal or anomalous behavior, then select Landé or custom g-factors.
- Provide upper and lower quantum numbers for the transition.
- Filter the displayed family if you only want σ+, π, or σ− components.
- Press the calculate button to see summary metrics, split levels, and grouped lines above the form.
- Use the CSV or PDF buttons to export the results table for notes, reports, or classwork.
FAQs
1) What does this calculator estimate?
It estimates magnetic splitting of atomic spectral lines, level energy shifts, frequency offsets, wavelength changes, and grouped transition components for allowed Zeeman transitions.
2) What is the difference between normal and anomalous modes?
Normal mode forces both g-factors to 1, which is useful for simple spin-free cases. Anomalous mode keeps state-dependent splitting through the Landé formula or custom g values.
3) Why are some transitions grouped together?
Different mJ pairs can produce identical line positions. Grouping reduces clutter and reports the shared wavelength with its degeneracy count and representative transitions.
4) Can I enter half-integer quantum numbers?
Yes. The form accepts half-integer S and J values, which are common in atomic spectroscopy. The calculator automatically generates matching mJ values in steps of one.
5) When should I use custom g-factors?
Use custom values when you already know measured or literature g-factors, or when the simple Landé expression is not the approximation you want.
6) Why does the calculator reject some J combinations?
It checks the dipole selection rule for ΔJ and blocks the forbidden 0 → 0 case. For Landé mode, it also checks whether L, S, and J form a valid state.
7) Are wavelength shifts exact or approximate here?
The page reports shifted wavelengths from the exact frequency relation λ′ = c/(ν0 + Δν). That is usually more reliable than using only the small-shift approximation.
8) Can I use these outputs for lab reports?
Yes, for quick estimates, comparisons, and clean exports. You should still confirm assumptions, constants, and transition assignments against your course notes or reference data.