Electron Configuration and Orbitals (Energy Levels)

Principal quantum number: n\in{1,2,3,…}, energy increases with increasing n; no zero level.
For each principal level n, there are sublevels: s, p, d, f. The number of sublevels in level n equals n.
Examples of sublevels in common levels:
- n=1:\ 1s
- n=2:\ 2s, 2p
- n=3:\ 3s, 3p, 3d
- n=4:\ 4s, 4p, 4d, 4f
Orbitals per sublevel:
- s: 1\ orbital
- p: 3\ orbitals
- d: 5\ orbitals
- f: 7\ orbitals
Max electrons per sublevel:
- s: 2\, (1\,\text{orbital})
- p: 6\, (3\,\text{orbitals})
- d: 10\, (5\,\text{orbitals})
- f: 14\, (7\,\text{orbitals})
Total electrons in level n: N_{max}(n)=2n^2
- n=1\Rightarrow 2, n=2\Rightarrow 8, n=3\Rightarrow 18
Level-to-sublevel order (illustrative): 1s\rightarrow 2s\rightarrow 2p\rightarrow 3s\rightarrow 3p\rightarrow 4s\rightarrow 3d\rightarrow 4p\rightarrow 5s\rightarrow 4d\rightarrow 5p\rightarrow \dots
Relationship observed: in each level, s\lt p\lt d\lt f in energy (generally), but exceptions exist (e.g., 4s is lower in energy than 3d).

Orbital = region where there is a high probability of finding an electron; not a fixed path.
s orbitals: spherical, one per sublevel.
p orbitals: three orbitals per sublevel, dumbbell-shaped along x, y, z axes.
d orbitals: five orbitals per sublevel, clover-shaped.
f orbitals: more complex shapes (not shown here).
Orbital shapes come from the Schrödinger equation; electron location is probabilistic (Heisenberg principle).
Electron clouds: density increases near nucleus for s orbitals; p/d/f shapes show regions where electrons are likely found.

Aufbau principle: fill lowest-energy sublevels first.
Pauli exclusion principle: an orbital holds at most two electrons, with opposite spins.
Hund's rule: electrons prefer to occupy separate orbitals within a sublevel with parallel spins before pairing.
Notation: sublevels occupied in order, e.g., 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, …

H: 1s^1
He: 1s^2
Li: 1s^2 2s^1
Be: 1s^2 2s^2
B: 1s^2 2s^2 2p^1
C: 1s^2 2s^2 2p^2
N: 1s^2 2s^2 2p^3
O: 1s^2 2s^2 2p^4
F: 1s^2 2s^2 2p^5
Ne: 1s^2 2s^2 2p^6
Na: 1s^2 2s^2 2p^6 3s^1
Mg: 1s^2 2s^2 2p^6 3s^2
Al: 1s^2 2s^2 2p^6 3s^2 3p^1
Si: 1s^2 2s^2 2p^6 3s^2 3p^2
P: 1s^2 2s^2 2p^6 3s^2 3p^3
S: 1s^2 2s^2 2p^6 3s^2 3p^4
Cl: 1s^2 2s^2 2p^6 3s^2 3p^5
Ar: 1s^2 2s^2 2p^6 3s^2 3p^6
K: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1
Ca: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2
Note: after Ar, 4s fills before 3d due to energy ordering in practice; this leads to the d-block (transition metals).

Periods reflect number of electron energy levels occupied:
- Period 1: only n=1 (H, He)
- Period 2: n=1 and n=2 (Li–Ne)
- Period 3: n=1–n=3 (Na–Ar)
- Period 4: beginning of n=4 (K–Ca) and so on
Groups reflect same valence electron count (same highest occupied energy level):
- 1A and 2A: valence in s; elements end in s sublevel (e.g., H, Li, Na, K; Be, Mg, Ca)
- 3A–8A: valence in p (3A: last is p for B, C, N, O, F, Ne; 8A: noble gases with 8 valence e− except He has 2)
Blocks (why named):
- S-block: groups 1–2; last occupied sublevel is s
- P-block: groups 13–18; last occupied sublevel is p
- D-block: transition metals; last electrons in d subshell (begins after Ca)
- F-block: lanthanides/actinides; last electrons in f subshell
Valence electrons (quick reference):
- 1A: 1 valence e−; 2A: 2; 3A: 3; 4A: 4; 5A: 5; 6A: 6; 7A: 7; 8A (noble gases): 8 (He = 2)
Concept: noble gases are chemically inert due to full valence shell (octet, except He with 2)

Orbitals per sublevel: s:\ 1,\ p:\ 3,\ d:\ 5,\ f:\ 7
Max electrons per sublevel: s:2,\ p:6,\ d:10,\ f:14
Total electrons in level n: N_{max}(n)=2n^2
Filling order (Aufbau) simplified: 1s\rightarrow 2s\rightarrow 2p\rightarrow 3s\rightarrow 3p\rightarrow 4s\rightarrow 3d\rightarrow 4p\rightarrow 5s\rightarrow 4d\rightarrow 5p\rightarrow \dots
Pauli exclusion: an orbital holds at most two electrons with opposite spins.
Hund's rule: within a sublevel, electrons occupy separate orbitals with parallel spins before pairing.
Schrödinger equation underpins orbital shapes; electron location is probabilistic, not a fixed path.