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GATE 2020 PH – Question 30

Atomic and Molecular Physics · Zeeman, Paschen-Back and Stark effects · 1 mark · Numerical answer

A hydrogenic atom is in a strong magnetic field. Neglect spin–orbit coupling. How many doubly degenerate states arise from its f level?

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Correct answer: 3 to 3

Explanation

For l = 3, $m_l=-3,-2,\ldots,3$ and $m_s=\pm1/2$. The Zeeman shift is $\mu_BB(m_l+2m_s)=\mu_BB(m_l\pm1)$. The two seven-value ladders overlap at shifts −2, −1, 0, 1 and 2 in units of $\mu_BB$. Each overlap corresponds to two distinct spin-orbital states, giving five doubly degenerate levels.

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