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Hydrogen in Electric and Magnetic Fields

Hydrogen levels n = 1..4 split under external fields. The primary scene is the physical term diagram, each Rydberg level fanning into sublevels as the magnetic (Zeeman, dE = mu_B B m_l) and electric (linear Stark for n >= 2) fields ramp, with the chosen transition drawn; beside it the synthetic spectrum shows the line splitting a spectrometer records (a normal-Zeeman triplet, a Stark multiplet), zoomed onto the multiplet. The ground state shows the textbook result: no first-order Stark shift (it has no permanent dipole), only a tiny negative quadratic one, while excited levels with degenerate l mix and split linearly in the field. Ramp B and the electric field and pick a transition to watch the normal-Zeeman triplet and the Stark multiplet form.

Figure 1. Hydrogen term diagram and synthetic spectrum under Stark and Zeeman fields.

WHAT TO TRY

  • Raise the magnetic field B: each level fans into Zeeman sublevels and the emission line splits into a multiplet, with the splitting growing linearly along the diagnostic line dE = 2 mu_B B.
  • Raise the electric field F: the Stark effect fans the levels too, but notice n=1 never splits. The ground state has no first-order Stark shift, the headline result flagged at the bottom of the ladder.
  • Switch the transition between Lyman, Balmer and Paschen lines: the arrow moves between levels and the synthetic spectrum recomputes its split components for that line.