Electron Shells and Carbon (Z=6)

Electron Shells: Fundamentals

• Atoms have electrons arranged in shells around the nucleus. Each shell is labeled by the principal quantum number $n$ (n = 1, 2, 3, …).
• The maximum number of electrons in shell $n$ is $2n^2$.
  • For $n=1$: maximum $2$ electrons.
  • For $n=2$: maximum $8$ electrons.
  • For $n=3$: maximum $18$ electrons.
• Within each shell, sublevels (s, p, d, f) contribute to the shell's capacity, but the overall per-shell limit is still $2n^2$.

Electron Configuration: Aufbau, Pauli, and Hund

• Aufbau principle: electrons fill the lowest-energy orbitals first.
• Pauli exclusion principle: no two electrons in an atom can have the same set of quantum numbers; each orbital holds at most two electrons with opposite spins.
• Hund’s rule: electrons occupy degenerate orbitals singly before pairing.
• Fill order (common sequence): 1s
  ightarrow 2s
  ightarrow 2p
  ightarrow 3s
  ightarrow 3p
  ightarrow 4s
  ightarrow 3d
  ightarrow 4p
  ightarrow 5s
  ightarrow 4d
  ightarrow 5p
  ightarrow 6s
  ightarrow 4f
  ightarrow 5d
  ightarrow 6p
  ightarrow 7s
  ightarrow ext{…}

Carbon Case Study (Z = 6)

• Nucleus has $Z=6$ protons; neutral atom has $E=6$ electrons.
• First shell (n = 1) holds up to $2$ electrons: $1s^2$.
• Outer/second shell (n = 2) holds the remaining $4$ electrons: $2s^2 2p^2$.
• Full electron configuration: $1s^2 2s^2 2p^2$.
• Valence electrons for carbon are the electrons in the outermost shell; here the outer shell contains $4$ electrons (4 valence electrons), contributing to carbon’s tetravalence.

Significance of the Shell Model

• The arrangement explains chemical bonding patterns and periodic trends.
• The capacity of the second shell is not always fully utilized in light elements (e.g., carbon uses 4 of the possible 8 in the second shell).
• Real-world relevance: carbon’s four valence electrons enable diverse organic chemistry and bonding versatility.

Notation and Key Numbers to Remember

• Maximum electrons in shell n: $2n^2$.
• First shell capacity: $2$; Second shell capacity (if filled): $8$; Third shell capacity (if filled): $18$.
• Carbon configuration: $1s^2 2s^2 2p^2$; total electrons: $Z=6$; valence electrons: $4$.

Quick Practice Questions

• Nitrogen (Z = 7): electron configuration = $1s^2 2s^2 2p^3$; second shell contains $5$ electrons.
• Neon (Z = 10): electron configuration = $1s^2 2s^2 2p^6$; second shell is full with $8$ electrons.