ATM-010 · Atoms and molecules Sample material

The hydrogen atom. Quantum numbers and magnetic moments

Energy levels and quantum numbers of the hydrogen atom, the electron's orbital mechanical and magnetic moments, the Bohr magneton, total mechanical and magnetic moments and the Stern–Gerlach experiment.

Estimated time: 3 h 4 activities

Learning objective

Learn to describe the states of the hydrogen atom by the quantum numbers $n$, $l$, $m$.
Explain the quantization of the orbital angular momentum and its projection.
Master the concepts of orbital magnetic moment, gyromagnetic ratio and Bohr magneton.
Analyse the essence and results of the Stern–Gerlach experiment.

Expected outcomes

Calculates $L = \hbar\sqrt{l(l+1)}$, $L_z = m\hbar$, $\mu_l = \mu_B\sqrt{l(l+1)}$.
Finds the total magnetic moment using the Landé factor.
Estimates the splitting and deflection of the beam in the Stern–Gerlach experiment.
Knows the method for measuring the specific charge of the electron experimentally.

Interactive modelOrbitals of the hydrogen atom

Activities

Lecture
Lecture · 1 h 20 min · required
Total mechanical and magnetic moments of the electron.
Practice · 1 h 20 min · required
Determination of the specific charge of the electron
Laboratory · 1 h 30 min · optional
Final test
Test · 20 min · required · pass ≥ 70%

Completion conditions

  • Lecture
  • Total mechanical and magnetic moments of the electron.
  • Final test — at least 70%