Potassium's D1 line ( ) is the transition

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Many-electron atoms and the periodic table · Radiative transitions, external fields and collisions

Reading the Spectrum, Ch Atoms in a magnetic field: moments, the Zeeman effect and the Paschen-Back limit

Problem

Potassium's D1 line (λ=769.90 nm\lambda = 769.90\,\mathrm{nm}) is the transition 4p 2P1/2→4s 2S1/24p\ ^2\mathrm{P}_{1/2} \to 4s\ ^2\mathrm{S}_{1/2}. A field B=0.80 TB = 0.80\,\mathrm{T} is applied along z^\hat z. ((a)) Calculate gJg_J for the upper level from the Lande formula (the lower level's gJ=2g_J = 2, as for any 2S1/2^2\mathrm{S}_{1/2} level). ((b)) List the mJm_J sublevel shifts of both levels in units of μBB\mu_{\rm B}B, and use ΔmJ=0,±1\Delta m_J = 0,\pm1 to find the allowed line shifts, also in units of μBB\mu_{\rm B}B. ((c)) Convert the shifts into wavelength separations from λ0=769.90 nm\lambda_0 = 769.90\,\mathrm{nm}, in nm.

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