Atomic Structure and Electron Configuration

Structure of the Atom

The atom consists of three fundamental particles:

| Particle | Symbol | Charge | Mass (amu) | Location | |----------|--------|--------|------------|----------| | Proton | p⁺ | +1 | 1.007 | Nucleus | | Neutron | n⁰ | 0 | 1.009 | Nucleus | | Electron | e⁻ | -1 | 0.00055 | Electron cloud |

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

| Sublevel | Number of Orbitals | Max Electrons | |----------|-------------------|---------------| | s ($\ell=0$) | 1 | 2 | | p ($\ell=1$) | 3 | 6 | | d ($\ell=2$) | 5 | 10 | | f ($\ell=3$) | 7 | 14 |

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)