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Scientific concepts, discoveries, and phenomena

Pauli Exclusion Principle (Pauli)

• Electrons cannot share the same orbital with the same spin.
• If two electrons occupy the same orbital, they must have opposite spins.

Electron spin and magnetic behavior

• Electron spin is described as rotation with two possible spin states (opposite directions of rotation).
• A spinning electron produces a magnetic field (modeled like a bar magnet).
• Opposite spin directions → magnetic fields in opposite directions.
• Example phenomenon (Stern–Gerlach-type idea):
  • In a magnetic field, a hydrogen atom with one electron can split such that half deflects toward the N pole and half toward the S pole, reflecting the two possible spin states.
• Note about field direction:
  • The magnetic-field direction associated with electron motion/spin is contrasted with magnetic field direction from current using Ampère’s law (with a sign difference attributed to electron flow vs conventional current).

Spin quantum numbers

• Spin quantum number values:
  • +1/2 (often described as “spin up” / counterclockwise)
  • −1/2 (often described as “spin down” / clockwise)
• To specify an electron state, four quantum numbers are used:
  1. principal quantum number
  2. azimuthal quantum number
  3. magnetic quantum number
  4. spin quantum number
• In a single atom, no two electrons can have exactly the same set of four quantum numbers.

Electron pairing vs. unpaired electrons

• Paired electrons:
  • two electrons in the same orbital with opposite spins
• Unpaired electrons:
  • only one electron in an orbital
• Opposite-spin magnetic fields are described as attracting, making paired electrons more stable.
• Same-spin in one orbital would create repulsive magnetic effects, making it unstable.
• Overall tendency emphasized:
  • Electrons fill orbitals to maximize unpaired electrons when energies are equal (Hund’s rule), delaying pairing.

Aufbau principle (order of orbital filling)

• Electrons fill orbitals in order of increasing energy:
  • Lowest-energy orbitals fill first.
• Orbital energy comparison (as described):
  • Energy increases with principal (n) and azimuthal (l) quantum numbers.
  • If the values are the same (e.g., comparison between 3p and 4s), the orbital with the larger principal quantum number (n) is higher in energy.

Hund’s rule (degenerate orbitals)

• For orbitals with the same energy (degenerate orbitals, e.g., the three p orbitals):
  • Electrons occupy orbitals singly first to maximize the number of unpaired electrons.
  • Only after each degenerate orbital has one electron do additional electrons pair up.

Example electron configurations mentioned

• Hydrogen (1 e⁻): 1s¹
• Helium (2 e⁻): 1s²
• Lithium (3 e⁻): 1s² 2s¹
• Beryllium (4 e⁻): 1s² 2s²
• Boron (5 e⁻): 1s² 2s² 2p¹
  • with 2p described as 2p¹ among three degenerate p orbitals
• Carbon (6 e⁻): 1s² 2s² 2p²
• Nitrogen (7 e⁻): 1s² 2s² 2p³
  • (max unpaired in p)
• Oxygen (8 e⁻): 1s² 2s² 2p⁴
  • (one p orbital becomes paired)

Listed/referenced researchers or sources

• Pauli (Pauli exclusion principle)
• Hund (Hund’s rule)
• Ampère (Ampère’s law; discussed for magnetic field direction comparison)
• German physicist Hund (same as Hund above)