Electron Configuration and Orbitals (Energy Levels)

Energy levels and sublevels

• 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).

Orbitals and shapes

• 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.

Electron configuration rules

• 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, …

Top-20 electron configurations (summary, patterns to memorize)

• 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, blocks, and valence electrons

• 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)

Quick reference formulas and concepts

• 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.