Electron configuration and orbital filling: Aufbau rule, La, Hg, Po

Understanding the Transcript Context

The transcript highlights common challenges in determining electron configurations, especially after xenon. Key issues include orbital filling sequences (s, p, d, f), correct placement of $4f$ and $5d$ electrons, and understanding the configuration of elements like Lanthanum (La) ($[\text{Xe}]\, 5d^{1}\ 6s^{2}$). The discussion also covers clarifying orbital diagram interpretation, resolving valence electron confusion for Polonium (Po, Z = 84) (which has $6s^{2}\ 6p^{4}$), and verifying total electron counts for Mercury (Hg, Z = 80).

Key Concepts for Electron Configuration

• Aufbau Principle & Madelung Rule: Electrons fill subshells in order of increasing energy ($n + l$). If $n + l$ values are equal, the subshell with lower $n$ fills first.
  • Typical Fill Order: $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p$
• Subshell Types: s ($l=0$, 1 orbital, 2 electrons), p ($l=1$, 3 orbitals, 6 electrons), d ($l=2$, 5 orbitals, 10 electrons), f ($l=3$, 7 orbitals, 14 electrons).
• Electron Configuration Notation:
  • Use noble gas core for simplification (e.g., $[\text{Xe}]\, 4f^{14}\ 5d^{10}\ 6s^{2}$ for Hg).
  • Total electrons in a neutral atom equals its atomic number (Z).
• Valence Electrons: For main-group elements, these are the outermost s and p electrons. Polonium (Po, Z = 84) has 6 valence electrons ($6s^{2}\ 6p^{4}$).
• Relevance: Electron configurations explain periodic trends, chemical reactivity, and element placement in the s-, p-, d-, f-blocks.
• Specific Examples:
  • Lanthanum (La): $[\text{Xe}]\, 5d^{1}\ 6s^{2}$
  • Mercury (Hg): $[\text{Xe}]\, 4f^{14}\ 5d^{10}\ 6s^{2}$
  • Polonium (Po): $[\text{Xe}]\, 4f^{14}\ 5d^{10}\ 6s^{2}\ 6p^{4}$

Madelung Rule: Details

• Rule: Orbitals fill by increasing $n + l$ value. If $n + l$ values are equal, the orbital with the lower principal quantum number ($n$) fills first (e.g., 4s ($n+l=4$) before 3d ($n+l=5$); 4d ($n+l=6$) before 5p ($n+l=6$) due to lower $n$).
• Typical Full Filling Sequence: $1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2, 4d^{10}, 5p^6, 6s^2, 4f^{14}, 5d^{10}, 6p^6, 7s^2, 5f^{14}, 6d^{10}, 7p^6$.

Practical Tips for Electron Configurations

• Start with a noble gas core (e.g., [Xe]) and add electrons according to the Aufbau/Madelung order.
• Carefully count electrons to ensure the total matches the atomic number (Z).
• Understand the definition of valence electrons: typically outermost s and p electrons for main-group elements. Be aware of context for elements like noble gases.
• Focus on the energy-based filling order rather than potentially confusing diagram paths.

Exam Success Takeaways

• Master the Aufbau/Madelung rule and the standard orbital filling sequence.
• Know benchmark configurations for La ($[\text{Xe}]\, 5d^{1}\ 6s^{2}$), Hg ($[\text{Xe}]\, 4f^{14}\ 5d^{10}\ 6s^{2}$), and Po ($[\text{Xe}]\, 4f^{14}\ 5d^{10}\ 6s^{2}\ 6p^{4}$).
• Understand why Po has 6 valence electrons and its group 16 placement.
• Efficiently use noble gas core notation.
• Practice verifying total electron counts and consistency with periodic table placement.