ATM-011 · Atoms and molecules Sample material

Electron spin. Fine structure

The Uhlenbeck–Goudsmit hypothesis, electron spin and its intrinsic magnetic moment, the spin gyromagnetic ratio, spin–orbit interaction, the fine structure of the hydrogen spectrum and the total mechanical and magnetic moments of an atom.

Estimated time: 3 h 4 activities

Learning objective

Explain on the basis of which experiments the concept of spin was introduced.
Learn to calculate the spin angular momentum, its projections and the intrinsic magnetic moment.
Understand the mechanism of spin–orbit interaction and the origin of fine structure.
Master the calculation of the total angular momentum j, the Landé factor g and the magnetic moment of an atom.

Expected outcomes

Knows that the spin quantum number is s = 1/2, the projections are m_s = ±1/2 and |S| = ħ√3/2.
Can explain that the spin gyromagnetic ratio is twice the orbital one (g_s ≈ 2).
Can find the possible values of j for given l and s and calculate |J| and g_J.
Can estimate the fine splitting of the sodium D doublet and of hydrogen levels.

Interactive modelThe Stern–Gerlach experiment and electron spin

Activities

Lecture
Lecture · 1 h 20 min · required
Solving problems on “Electron spin. Fine structure”
Practice · 1 h 20 min · required
The Bohr magneton. Electron spin
Self-study · 6 h 10 min · optional
Final test
Test · 20 min · required · pass ≥ 70%

Completion conditions

  • Lecture
  • Solving problems on “Electron spin. Fine structure”
  • Final test — at least 70%