Key Definitions

• Atomic number ($Z$): Number of protons (defines the element)
• Mass number ($A$): Total protons + neutrons
• Isotopes: Atoms of same element with different numbers of neutrons

Notation: $^A_ZX$ where $X$ is element symbol

Example: $^{12}_6C$ (Carbon-12) has 6 protons, 6 neutrons, 6 electrons

Quantum Numbers

Four quantum numbers describe each electron in an atom:

1. Principal Quantum Number ($n$)

• Values: $n = 1, 2, 3, 4, ...$
• Meaning: Energy level (shell)
• Capacity: Maximum $2n^2$ electrons per level

2. Angular Momentum Quantum Number ($\ell$)

• Values: $\ell = 0$ to $n-1$
• Meaning: Sublevel (subshell) shape
  • $\ell = 0$: s orbital (spherical)
  • $\ell = 1$: p orbital (dumbbell)
  • $\ell = 2$: d orbital (cloverleaf)
  • $\ell = 3$: f orbital (complex)

3. Magnetic Quantum Number ($m_\ell$)

• Values: $-\ell$ to $+\ell$ (including 0)
• Meaning: Orbital orientation in space
• Number of orbitals: $2\ell + 1$

4. Spin Quantum Number ($m_s$)

• Values: $+\frac{1}{2}$ or $-\frac{1}{2}$
• Meaning: Electron spin direction
• Pauli Exclusion Principle: No two electrons can have the same four quantum numbers

Orbital Capacity

Electron Configuration

Electron configuration shows how electrons are distributed among orbitals.

Order of Filling (Aufbau Principle)

Electrons fill orbitals in order of increasing energy:

$1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p$

Memory aid: Use the diagonal rule or periodic table

Notation

Full configuration: List all sublevels with number of electrons

Example: Oxygen (8 electrons) $1s^2 2s^2 2p^4$

Noble gas configuration: Use previous noble gas in brackets

Example: Calcium (20 electrons) $[Ar] 4s^2$

Orbital diagram: Show each orbital as a box with electron spins

Three Key Rules

1. Aufbau Principle

Electrons fill lowest energy orbitals first.

2. Pauli Exclusion Principle

Maximum 2 electrons per orbital, with opposite spins.

3. Hund's Rule

When filling orbitals of equal energy (like three p orbitals), place one electron in each orbital before pairing.

Example: Nitrogen (7 electrons)

2p orbitals: ↑ ↑ ↑ (one electron in each)

NOT: ↑↓ ↑ (incorrect - violates Hund's rule)

Electron Configurations of Ions

Cations (positive ions)

Remove electrons from highest $n$ value first (usually outermost s)

Example: Fe → Fe²⁺

• Fe: $[Ar] 4s^2 3d^6$
• Fe²⁺: $[Ar] 3d^6$ (remove 4s² electrons)

Anions (negative ions)

Add electrons following normal filling order

Example: O → O²⁻

• O: $1s^2 2s^2 2p^4$
• O²⁻: $1s^2 2s^2 2p^6$ (add 2 electrons to 2p)

Exceptions to Filling Order

Some elements have anomalous electron configurations for extra stability:

Chromium (Cr):

• Expected: $[Ar] 4s^2 3d^4$
• Actual: $[Ar] 4s^1 3d^5$ (half-filled d sublevel is more stable)

Copper (Cu):

• Expected: $[Ar] 4s^2 3d^9$
• Actual: $[Ar] 4s^1 3d^{10}$ (filled d sublevel is more stable)

Why: Half-filled and fully-filled sublevels have extra stability.

Valence Electrons

Valence electrons are electrons in the outermost shell (highest $n$).

They determine:

• Chemical properties
• Bonding behavior
• Reactivity

Example: Nitrogen $[He] 2s^2 2p^3$

• Valence electrons: 5 (in $n=2$ shell)

Core vs. Valence Notation

Core electrons: Inner electrons (represented by noble gas) Valence electrons: Outer electrons (written out)

Example: Phosphorus (P)

• Full: $1s^2 2s^2 2p^6 3s^2 3p^3$
• Noble gas: $[Ne] 3s^2 3p^3$
• Core: [Ne] (10 electrons)
• Valence: $3s^2 3p^3$ (5 electrons)

Neutral sulfur has 16 electrons (same as protons).

Step 2: Fill orbitals in order

Order: 1s, 2s, 2p, 3s, 3p

• 1s: 2 electrons → $1s^2$ (total: 2)
• 2s: 2 electrons → $2s^2$ (total: 4)
• 2p: 6 electrons → $2p^6$ (total: 10)
• 3s: 2 electrons → $3s^2$ (total: 12)
• 3p: 4 electrons → $3p^4$ (total: 16) ✓

Answer: $1s^2 2s^2 2p^6 3s^2 3p^4$

Noble gas notation: $[Ne] 3s^2 3p^4$

Verification:

• Total electrons: $2 + 2 + 6 + 2 + 4 = 16$ ✓
• Valence electrons: 6 (matches Group 16) ✓