Structure 1.3.5 — Electron Configuration, Orbitals and Principles

Each orbital is a region of space around the nucleus where there is a high probability of finding an electron. These orbitals are defined energy states within sublevels and can hold a maximum of two electrons with opposite spin.

Principles:

• Pauli Exclusion Principle: No two electrons in the same atom can have the same set of quantum numbers – each orbital holds a maximum of two electrons with opposite spins.
• Hund’s Rule: When electrons occupy orbitals of the same energy (degenerate orbitals), they fill singly first with parallel spins before pairing occurs.
• Aufbau Principle: Electrons fill lower energy orbitals first before occupying higher ones.

Sublevels and Number of Orbitals:

• s sublevel: 1 orbital → max 2 electrons
• p sublevel: 3 orbitals → max 6 electrons
• d sublevel: 5 orbitals → max 10 electrons
• f sublevel: 7 orbitals → max 14 electrons

Each main energy level (n) contains a specific number of sublevels, which are split into orbitals:

• n = 1 → 1s
• n = 2 → 2s, 2p
• n = 3 → 3s, 3p, 3d
• n = 4 → 4s, 4p, 4d, 4f

Electron configurations up to atomic number \( Z = 36 \) (Krypton) can be determined by applying these rules to distribute electrons among the orbitals in increasing energy order.

Applying Electron Configuration Rules (Z ≤ 36)

To deduce electron configurations for atoms and ions (up to atomic number 36), we apply three key principles:

1. Aufbau Principle: Electrons fill orbitals starting with the lowest available energy levels before moving to higher ones.

2. Hund’s Rule: Within a sublevel, electrons fill degenerate orbitals singly first (with parallel spins), and only pair when no empty orbital remains.

3. Pauli Exclusion Principle: Each orbital can hold a maximum of two electrons with opposite spins.

Order of Orbital Filling (up to Z = 36):

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p

Subshell Capacities: s (2 electrons), p (6), d (10), f (14)

Notice that within the same principal level, orbitals with a lower value of l have lower energy (E) and therefore, are filled first. So, for a given value of n:

$\text{E (s orbital) < E ( p orbital) < E (d orbital) < E ( f orbital)}$

Full and Condensed Electron Configurations

1. Full Electron Configuration: Lists all orbitals and the number of electrons in each. Example for sulfur (Z = 16):

\( 1s^2\, 2s^2\, 2p^6\, 3s^2\, 3p^4 \)

2. Condensed Electron Configuration (Noble Gas Core):

Use the configuration of the nearest noble gas in brackets, then continue from there:

Sulfur (Z = 16): \( [\text{Ne}]\, 3s^2\, 3p^4 \)

Why Use Condensed Configurations?

• Saves time and space when writing configurations

Orbital Diagrams (Arrow-in-Box)

Orbital diagrams show how electrons are arranged within orbitals, respecting Hund’s rule and Pauli’s exclusion principle

Stability of Half-Filled and Filled Sublevels:

The electron jumps from the $4s$ level to the $3d$ level compensating the energy uphill by a stabilization associated with half-filled orbitals.

Example: Nitrogen (Z = 7)

Electron configuration: \( 1s^2\, 2s^2\, 2p^3 \)

• Each box represents an orbital (e.g., 2p has three boxes: \( p_x \), \( p_y \), \( p_z \))
• Each arrow represents an electron (↑ = spin up, ↓ = spin down)
• Electrons fill degenerate orbitals singly before pairing (Hund’s Rule)

Additional Examples:

1. Sodium (Z = 11)

Full: \( 1s^2\, 2s^2\, 2p^6\, 3s^1 \)
Condensed: \( [\text{Ne}]\, 3s^1 \)

2. Oxygen (Z = 8)

Full: \( 1s^2\, 2s^2\, 2p^4 \)
Condensed: \( [\text{He}]\, 2s^2\, 2p^4 \)

3. Chromium (Z = 24) — Exception

Expected: \( [\text{Ar}]\, 4s^2\, 3d^4 \)
Actual: \( [\text{Ar}]\, 4s^1\, 3d^5 \)

Reason: A half-filled d-subshell (3d⁵) provides extra stability.

4. Copper (Z = 29) — Exception

Expected: \( [\text{Ar}]\, 4s^2\, 3d^9 \)
Actual: \( [\text{Ar}]\, 4s^1\, 3d^{10} \)

Reason: A fully-filled d-subshell (3d¹⁰) is more stable than expected configuration.

Tips:

• Always write in order of increasing energy, not by numerical sequence of shells.
• Use noble gas shorthand for longer configurations: e.g., \( [\text{Ne}]\, 3s^2\, 3p^4 \)
• For ions:
  • Remove electrons from the highest energy level (4s before 3d for transition metals).