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Spin and Pauli exclusion principle

Formalism and applications · Physics

Study notes

Worked example: How does the Pauli principle determine the electron configuration of carbon (6 electrons)? Step 1: Energy shells fill in order 1s, 2s, 2p. Each spatial orbital holds at most 2 electrons (spin up + spin down) by Pauli. Step 2: 1s takes 2 electrons (↑↓). Remaining: 4. Step 3: 2s takes 2 electrons (↑↓). Remaining: 2. Step 4: 2p has three orbitals (px, py, pz). Hund's rule (from Pauli + repulsion): the 2 remaining electrons go into different orbitals with parallel spins: 2px¹ 2py¹. Step 5: Configuration: 1s² 2s² 2p² — with two unpaired electrons, explaining carbon's valency of 4 (it can share/promote to make 4 bonds). Conclusion: one exclusion rule generates the entire periodic table's structure — chemistry is applied Pauli principle.

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