What is the Zeeman effect?

The Zeeman effect is the splitting or shifting of atomic spectral lines when the atom is placed in an external magnetic field. The magnetic field breaks the degeneracy of states with different magnetic quantum numbers m_J, causing them to shift in energy by ΔE = g × m_J × μ_B × B.

What is the difference between normal and anomalous Zeeman effect?

The normal Zeeman effect occurs when the total spin S = 0 so the Landé g-factor equals exactly 1, producing three evenly spaced lines. The anomalous Zeeman effect occurs when S ≠ 0; the g-factor deviates from 1, producing more complex patterns. This calculator handles both by letting you set g freely.

What is the Bohr magneton?

The Bohr magneton μ_B = eℏ / (2m_e) ≈ 9.2741 × 10⁻²⁴ J/T is the natural unit of magnetic moment for an electron. It sets the scale of the energy splitting per tesla per unit of m_J.

What is the Landé g-factor?

The Landé g-factor (or g_J) accounts for the relative contributions of orbital (L) and spin (S) angular momentum to the total magnetic moment. For pure orbital angular momentum g = 1; for pure spin g ≈ 2. In general, g_J = 1 + [J(J+1) + S(S+1) − L(L+1)] / [2J(J+1)].

How is the wavelength shift calculated?

Starting from E = hc/λ, differentiating gives |Δλ| = λ² × |ΔE| / (hc), where λ is the reference wavelength, h = 6.626 × 10⁻³⁴ J·s, and c = 2.998 × 10⁸ m/s. A positive ΔE (higher-energy sub-level) corresponds to a blue shift; negative ΔE gives a red shift.

What units should I use for the inputs?

Enter B in tesla (T), m_J as a dimensionless number (integer or half-integer), g-factor dimensionless, and the reference wavelength in nanometres (nm). Results are given in joules (J), electron-volts (eV), and nanometres (nm).

Zeeman Splitting Calculator

Name: Zeeman Splitting Calculator
Availability: InStock
Author: Nham Vu

Enter magnetic field strength, magnetic quantum number, and g-factor to calculate Zeeman energy and wavelength splitting of a spectral line.

Inputs

Magnetic Field Strength (B, tesla)

Magnetic Quantum Number (m_J)

Integer or half-integer, e.g. −1, 0, 1, or −0.5, 0.5

Landé g-factor (g_J)

Use 1 for normal Zeeman effect; ~2 for pure spin

Reference Wavelength (λ₀, nm)

Unperturbed spectral line wavelength

Enter values on the left and click Calculate

Quick Examples

Summary

Enter magnetic field strength, magnetic quantum number, and g-factor to calculate Zeeman energy and wavelength splitting of a spectral line.

How it works

Enter the magnetic field strength B in tesla.
Enter the magnetic quantum number (m_l or m_J — any integer or half-integer).
Optionally enter the Landé g-factor (default 1 for the normal Zeeman effect).
Enter the reference wavelength of the unperturbed spectral line in nm.
Click Calculate to get ΔE in joules and eV, and the wavelength shift Δλ in nm.

Use cases

Verify Zeeman splitting homework problems in atomic physics courses.
Estimate the spectral resolution needed to observe a Zeeman-split line at a given field.
Compare normal vs. anomalous Zeeman shift for different g-factors.
Convert between energy splitting and wavelength shift for lab spectroscopy.
Explore how field strength scales the splitting across different B values.
Compute the splitting for multiple sub-levels (different m_J values) at once.

Frequently Asked Questions

Last updated: 2026-07-27 · Reviewed by Nham Vu