Anomalous Zeeman Effect

Zeeman and Paschen Back Effect Diagram
Definition:
The Anomalous Zeeman Effect is the splitting of spectral lines into more than three components when an atom is placed in an external magnetic field, typically observed in atoms having unpaired electron spin and non-zero total angular momentum.

Explanation :

  1. In the normal Zeeman effect only orbital angular momentum is considered and energy levels split into three (a triplet) because of simple magnetic interaction.
  2. Most atoms, however, have both orbital L and spin S angular momenta which couple to give total angular momentum J. The interaction with the magnetic field depends on the Landé g-factor (gJ), not just on orbital motion.
  3. Each atomic level splits into (2J + 1) magnetic sublevels labelled by mJ, producing multiple components in the observed spectral lines. Selection rules (ΔmJ = 0, ±1) determine which transitions are allowed, giving a complex pattern of π and σ lines.
  4. The anomalous effect thus reveals the role of electron spin and the vector coupling of L and S, and was historically important evidence for the existence of electron spin and for quantum theory.

Key formula:

\[\Delta E = \mu_B\, g_J\, B\, m_J\]

where \(\mu_B\) is the Bohr magneton, \(B\) is the magnetic field, \(g_J\) is the Landé g-factor, and \(m_J\) is the magnetic quantum number.

Paschen Back Effect :

In very strong magnetic fields, the coupling between orbital angular momentum \(L\) and spin \(S\) breaks down. The magnetic interaction becomes dominant compared to spin orbit coupling, causing \(L\) and \(S\) to align independently with the field. This leads to a simpler splitting pattern than the anomalous Zeeman effect, similar to the normal Zeeman effect.

This occurs When magnetic energy \(\mu_B B\) is much greater than spin orbit interaction energy.