Electron Orbital Magnetic Moments, Quantization, and Zeeman Splitting

All flashcards

How is an electron’s orbital magnetic-moment magnitude related to its angular-momentum magnitude?

For electron mass $m_e$ and charge magnitude $e$, $\mu=(e/2m_e)L$.

What is the Bohr magneton?

The unit $\mu_B=e\hbar/(2m_e)$, approximately $9.3\times10^{-24}\,\text{J/T}$.

What do the orbital quantum numbers $l$ and $m$ determine?

$l$ determines orbital angular-momentum magnitude; $m$ determines its $z$-projection.

Why does an electron’s orbital magnetic moment point opposite to its angular momentum?

The electron’s negative charge gives $\vec{\mu}=-(e/2m_e)\vec{L}$.

What contribution to an atom’s magnetic moment is excluded from the orbital-only description?

The contribution from electron spin.

Quiz questions

1. Which expression gives the magnitude of orbital angular momentum for orbital quantum number $l$?Answer: $L=\sqrt{l(l+1)}\,\hbar$
2. For an electron in a $d$ state, where $l=2$, what is the orbital magnetic-moment magnitude?Answer: $\sqrt{6}\,\mu_B$
3. An external magnetic field points along $+z$. What is the electron’s orbital magnetic energy for magnetic quantum number $m$?Answer: $U=m\mu_BB$
4. What does the Zeeman effect describe?Answer: Splitting of atomic energy levels in an external magnetic field.
5. How can the separation of Zeeman spectral components be used?Answer: It can help determine the strength of the external magnetic field.