An orbital is a region of space around the nucleus of an atom where there is a high probability of finding an electron. Orbitals are described by quantum mechanics and result from solving the Schrödinger equation for electrons in atoms.
Key Concepts:
Orbitals are not orbits—they do not depict a fixed path, but rather a cloud-like region where electrons are likely to be found.
Each orbital can hold a maximum of 2 electrons with opposite spins.
Orbitals have specific shapes, energies, and are described by quantum numbers.
Types of Orbitals and Their Shapes:
Orbital Type
Shape
Max Electrons
Found In Energy Levels
s
Spherical
2
All levels (1, 2, 3…)
p
Dumbbell
6 (3 orbitals × 2)
Levels 2 and higher
d
Cloverleaf
10 (5 orbitals × 2)
Levels 3 and higher
f
Complex
14 (7 orbitals × 2)
Levels 4 and higher
Electron Configuration and Orbitals:
Electrons fill orbitals in a specific order based on their energy: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s… (This is called the Aufbau principle.)
The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers (i.e., only two electrons per orbital, with opposite spins).
Hund’s rule states that electrons will fill degenerate orbitals (e.g., the three 2p orbitals) one at a time with parallel spins before pairing up.
Quantum Numbers and Orbitals:
Quantum Number
Symbol
Describes
Principal
n
Energy level and size of the orbital
Angular momentum
l
Shape of the orbital (s = 0, p = 1, d = 2, f = 3)
Magnetic
mₗ
Orientation of the orbital in space
Spin
mₛ
Spin direction of the electron (±½)
Visual Summary:
Orbital
Shape
Notes
1s
Sphere
Closest to nucleus
2p
Dumbbell
Three orientations (px, py, pz)
3d
Cloverleaf
Five orientations, complex shapes
4f
Multi-lobed
Seven orientations, very complex
Importance of Orbitals:
Determine how atoms bond (e.g., hybrid orbitals in covalent bonding)
Explain the geometry of molecules (e.g., tetrahedral, linear)
Predict magnetic properties (e.g., paramagnetic vs. diamagnetic)
