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In the weak-field Zeeman effect, spin-orbit coupling keeps $L,S,J$ good and a level shifts by ${\mu }_B{g}_{J}B{m}_J$. At fields large compared with fine-structure coupling but still within the linear electronic Zeeman approximation, $L$ and $S$ decouple: the Paschen-Back effect gives shifts ${\mu }_{B}B(m_L+2m_S)$. Electric-dipole transitions obey $\Delta m_L=0,\pm 1$, $\Delta m_S=0$ in that limit, recovering an orbital triplet pattern. Intermediate fields mix the coupled states.

For the weak-field sodium D-line Zeeman pattern, the given Landé g-factor formula givesAllowed photon shifts are $\delta E={\mu }_{B}B(g_u{m}_u-2m_l)$ with $m_u-m_l=0,\pm 1$. ThusThese are the four- and six-component patterns. Both $\pi$ and $\sigma$ components are represented, so an observation strictly along the field, which removes $\pi$ emission, would not show this complete pattern. Hyperfine structure is neglected.

To determine the magnetic field from a Zeeman diagram, the unsplit separation provides its energy scale:The smallest adjacent split spacing $s_E=2{\mu }_B{B}_1/3$ is approximately $0.070$ of that separation in the sketch. ThereforeThis is a graphical estimate; the drawing does not warrant high precision. Its splitting energy is small compared with $\Delta E_D$, consistent with the weak-field approximation.

For Doppler resolution of a Zeeman pattern, thermal velocities give Gaussian Doppler broadening with widthAt $350\mathrm{K}$, the photon-energy FWHM near $589\mathrm{nm}$ is $5.88\times 10^{-6}\mathrm{eV}$. Equating the smallest adjacent Zeeman spacing to this width gives $B\sim 0.15\mathrm{T}$ for loss of individually resolved components. There is no sharp Gaussian resolution threshold; using whole-pattern width instead gives a smaller field of order $0.03$–$0.04\mathrm{T}$ for complete disappearance into a single envelope. Instrumental and collisional broadening would also affect the estimate.