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): $1s <br /> ightarrow 2s <br /> ightarrow 2p <br /> ightarrow 3s <br /> ightarrow 3p <br /> ightarrow 4s <br /> ightarrow 3d <br /> ightarrow 4p <br /> ightarrow 5s <br /> ightarrow 4d <br /> ightarrow 5p <br /> ightarrow 6s <br /> ightarrow 4f <br /> ightarrow 5d <br /> ightarrow 6p <br /> ightarrow 7s <br /> ightarrow ext{…}$

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.