24 5.3 Hund's rule
Electrons do not pair in a sublevel until each orbital of the sublevel contains one electron (orbitals are filled singly first, with parallel spins).
- Why?
- The orbitals of one sublevel have the same energy.
- Two electrons placed in the same orbital repel each other, increasing the energy of the atom; electrons spread over separate orbitals with parallel spins give the atom the maximum stability.
- Nitrogen ₇N: 1s² 2s² 2p³. The three 2p electrons occupy three different orbitals: 2px¹ 2py¹ 2pz¹ (all spins parallel).
- Oxygen ₈O: 2p⁴. Three electrons go singly into px, py, pz; the fourth could either pair in a p orbital or go to the higher sublevel 3s. Pairing in the 2p orbital costs less energy than moving to the higher 3s, so it pairs: 2px² 2py¹ 2pz¹.
Orbital box diagrams for the last level:
- N: 2s [↑↓]; 2p [↑][↑][↑]
- O: 2s [↑↓]; 2p [↑↓][↑][↑]
- F: 2s [↑↓]; 2p [↑↓][↑↓][↑]
- Ne: 2s [↑↓]; 2p [↑↓][↑↓][↑↓]
✍️ Worked examples
Worked example 5.4 — unpaired electrons.
- Carbon ₆C: 1s² 2s² 2px¹ 2py¹: two unpaired electrons.
- Oxygen: two unpaired (2py, 2pz).
- Fluorine: one unpaired.
- Neon: none.
- Phosphorus ₁₅P (3p³): three unpaired electrons.
Worked example 5.5 — which diagram is correct for oxygen?
- 2p must show one pair and two single electrons with parallel spins: [↑↓][↑][↑].
- A diagram showing [↑↓][↑↓][ ] (two pairs, one empty orbital) violates Hund's rule.
Worked example 5.6 — find the atomic number. An atom has the configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹. The sum of the electrons is 19, so Z = 19 (potassium). In its ground state, its last electron has n = 4, ℓ = 0, mℓ = 0, ms = +½.