Beyond the Bohr Model

The quantum mechanical model describes electrons as existing in probability clouds called orbitals, not fixed paths. Electrons have certain allowed energies, and their exact locations can't be pinpointed—only the probability of finding them in a region.

Electron Configuration

• Electrons fill orbitals in a specific order (Aufbau principle).
• Pauli exclusion principle: No two electrons can have the same set of quantum numbers.
• Hund's rule: Electrons fill degenerate orbitals singly first.

Quantum Numbers

There are four quantum numbers that describe each electron:

1. Principal (\( n \)): Energy level.
2. Angular momentum (\( l \)): Shape of the orbital.
3. Magnetic (\( m_l \)): Orientation.
4. Spin (\( m_s \)): Direction of spin.

Real-World Relevance

Quantum mechanics explains why elements emit unique colors in fireworks and enables technologies like lasers and MRI machines.