Concept of Quantization in Quantum Chemistry
Quantization means that certain properties of microscopic particles (like electrons, atoms, and molecules) can only take specific, discrete values, not a continuous range.
1. Energy Levels are Quantized
- In classical physics, a particle can have any energy.
- In quantum chemistry, electrons in atoms and molecules can occupy only fixed energy levels.
- Example: In a hydrogen atom, the electron’s energy is restricted to values defined by the principal quantum number n = 1, 2, 3…
2. Orbitals and Quantum Numbers
- Electrons exist in orbitals described by wavefunctions.
- Each orbital is defined by quantum numbers (n, l, m, s).
- These quantum numbers are quantized → only certain allowed values.
3. Quantization of Other Properties
- Angular Momentum: Electrons in orbitals have quantized angular momentum (only certain multiples of ħ).
- Vibrations of molecules: Molecular bonds vibrate at specific frequencies, not continuously.
- Rotations of molecules: Molecules rotate only at fixed quantized energy levels.
4. Why Quantization Happens
- Solving the Schrödinger equation for atoms/molecules gives wave-like solutions.
- Only wavefunctions that “fit” the boundary conditions are valid → this restricts energy to discrete values.
- Similar to how a guitar string can vibrate only in certain harmonics (not at any frequency).
5. Real-Life Examples
- Spectroscopy: Absorption/emission lines appear at discrete wavelengths → direct evidence of quantization.
- Photoelectric effect: Electrons are ejected only if light has a minimum quantized energy (a photon with E = hν).
- Lasers: Work because atoms/molecules undergo quantized electronic transitions.
In short: Quantization in quantum chemistry means that energy, angular momentum, and other properties of particles are restricted to discrete values, not continuous ones. This concept explains why atoms have specific energy levels and why we observe line spectra instead of continuous ones.