In quantum mechanics, orbitals are regions in space where an electron is most likely to be found. They come directly from solving the Schrödinger equation for atoms.
Instead of electrons moving in fixed paths (like planets around the Sun in Bohr’s model), quantum mechanics says:
Electrons exist in “cloud-like” regions called orbitals.
How orbitals are described:
- By wave functions (Ψ):
- Each orbital is a mathematical solution (wave function) of the Schrödinger equation.
- The square of the wave function (Ψ²) gives the probability density of finding the electron in that region.
- By quantum numbers:
- Orbitals are described using three quantum numbers:
- n (principal quantum number): size & energy level.
- l (azimuthal quantum number): shape (s, p, d, f…).
- mₗ (magnetic quantum number): orientation in space.
- Orbitals are described using three quantum numbers:
- By shape and type:
- s orbital → spherical.
- p orbitals → dumbbell-shaped.
- d orbitals → cloverleaf-shaped.
- f orbitals → complex shapes.
- By energy:
- Orbitals with higher n are larger and higher in energy.
- Subshell order (Aufbau principle): 1s → 2s → 2p → 3s → 3p → 4s → 3d …
In short:
Orbitals in quantum mechanics are probability regions for electrons, defined by quantum numbers and wave functions, not fixed paths. They explain why atoms bond, how electrons arrange themselves, and the entire structure of the periodic table.