Structure 1.3.4 — Sublevels and Atomic Orbitals

Main Energy Levels and Sublevels

Each main energy level \( n \) is divided into sublevels: s, p, d, and f.

• s-sublevel: holds 1 orbital (max 2 electrons)
• p-sublevel: holds 3 orbitals (max 6 electrons)
• d-sublevel: holds 5 orbitals (max 10 electrons)
• f-sublevel: holds 7 orbitals (max 14 electrons)

The order of sublevel energy increases as follows:

$1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s…$

Shape and Orientation of Orbitals

1. s orbital:

• Shape: spherical
• Orientation: only one possible orientation (symmetric in all directions)
• Present in all main energy levels (\( n = 1 \) and above)

2. p orbitals:

• Shape: dumbbell-shaped
• Three orientations: along the x, y, and z axes → called \( p_x \), \( p_y \), and \( p_z \)
• Present from the second energy level (\( n = 2 \)) onwards

3. d orbitals:

• Shape: cloverleaf-shaped (four of them) and one with a donut-shaped ring
• Five orientations: \( d_{xy} \), \( d_{yz} \), \( d_{xz} \), \( d_{x^2 – y^2} \), and \( d_{z^2} \)
• Present from the third energy level (\( n = 3 \)) onwards

4. f orbitals:

• Shape: complex and multi-lobed structures
• Seven orientations: e.g., \( f_{xyz} \), \( f_{z^3} \), etc.
• Present from the fourth energy level (\( n = 4 \)) onwards