Engineering & Science
Normal Zeeman Effect: Bohr Magneton Energy & Spectral Wavelength Splitting
Calculate Zeeman magnetic sublevel energy splitting delta_E = mu_B * B (in micro-electronvolts, mu_B = 57.8838 ueV/T) and Lorentz triplet wavelength shift delta_lambda = 4.66864e-5 * B * lambda_0^2 (in picometers).
Measure solar sunspot and laboratory magnetic fields directly from spectral line splitting!
Pieter Zeeman (1896, Nobel Prize 1902) discovered that placing emitting atoms inside an external magnetic field B (Tesla) splits spin-singlet (S = 0, Landé g_J = 1) spectral transitions into a classic Lorentzian triplet (sigma-, pi, sigma+) separated in energy by the CODATA Bohr Magneton mu_B = e * hbar / (2 * m_e) = 57.8838 ueV/T (micro-electronvolts per Tesla, corresponding to 13.996 GHz/T or 0.466864 cm^-1/T)!
Converting that wavenumber shift delta_nu_bar = 0.466864 * B (cm^-1) at transition wavelength lambda_0 (nm) via |delta_lambda| = lambda_0^2 * delta_nu_bar yields the exact wavelength shift between the central pi line and each outer sigma component in picometers (pm): delta_lambda_pm = 0.0000466864 * B * (lambda_0_nm ^ 2)! For the classic red Cadmium singlet line lambda_0 = 643.847 nm inside a B = 1.50 T electromagnet, mu_B * B = 86.83 ueV and each sigma wing shifts by +/-29.03 pm (total outer doublet span = 58.06 pm)!
| Magnetic Field Scenario (Cd Red Singlet 643.847 nm) | Zeeman Energy Shift muB * B (ueV) | Single-Wing Shift d_lambda (pm) | Spectroscopic Resolution |
|---|---|---|---|
| Lab Electromagnet (B = 1.50 T) | 86.83 ueV | 29.03 pm | Resolved by Fabry-Pérot Etalon |
| Solar Sunspot Umbra (B = 0.30 T) | 17.37 ueV | 5.81 pm | Magnetogram Stokes-V Splitting |
| Invalid Negative Field or Wavelength | Guarded Input Error | "Invalid Zeeman Inputs" | Requires B >= 0 and lambda0 > 0 |
Normal Zeeman Energy Splitting delta_E (ueV) = 57.8838 * B
Multiplies magnetic flux density B (Tesla, cell B2) by the Bohr magneton mu_B = 57.883818 ueV/T.
=IF(OR(B2 < 0, B3 <= 0), "Invalid Zeeman Inputs", ROUND(57.8838 * B2, 2))Normal Zeeman Spectral Triplet Wing Shift delta_lambda (pm) = 0.0000466864 * B * lambda_0^2
Computes the +/- picometer shift of the delta_m_L = +/-1 sigma components for rest wavelength B3 (nm).
=IF(OR(B2 < 0, B3 <= 0), "Invalid Zeeman Inputs", ROUND(0.0000466864 * B2 * (B3 ^ 2), 2))Try the example
Use the original values or change them to test your understanding.