Hydrogen's level has a fine-structure interval of

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · 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

Hydrogen's n=2n = 2 level has a fine-structure interval of 0.365 cm−10.365\,\mathrm{cm^{-1}}, and sodium's 3p3p level one of 17.2 cm−117.2\,\mathrm{cm^{-1}}. Both sit in a field B=3.0 TB = 3.0\,\mathrm{T}. Take μBB/hc=0.467 cm−1\mu_{\rm B}B/hc = 0.467\,\mathrm{cm^{-1}} per tesla. ((a)) Find μBB\mu_{\rm B}B as a multiple of each interval, and decide whether the field is weak or strong for each level. ((b)) For a 2p2p electron in this field, list the six (ml,ms)(m_l, m_s) states with their shifts (ml+2ms)μBB(m_l + 2m_s)\mu_{\rm B}B in cm−1\mathrm{cm^{-1}}, and count the distinct values. ((c)) For a line whose upper and lower levels are both in the strong-field regime, how many components appear, and how far apart are neighbouring components, in cm−1\mathrm{cm^{-1}}?

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